diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 44d3d840016fe..b7961b28f0252 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -15,7 +15,7 @@
 import itertools
 import sys
 from textwrap import dedent
-from typing import FrozenSet, List, Optional, Set, Tuple, Type, Union
+from typing import FrozenSet, List, Optional, Sequence, Set, Tuple, Type, Union
 import warnings
 
 import numpy as np
@@ -80,7 +80,7 @@
 )
 from pandas.core.dtypes.missing import isna, notna
 
-from pandas._typing import Axes, Dtype
+from pandas._typing import Axes, Dtype, FilePathOrBuffer
 from pandas.core import algorithms, common as com, nanops, ops
 from pandas.core.accessor import CachedAccessor
 from pandas.core.arrays import Categorical, ExtensionArray
@@ -559,14 +559,14 @@ def _is_homogeneous_type(self) -> bool:
     # ----------------------------------------------------------------------
     # Rendering Methods
 
-    def _repr_fits_vertical_(self):
+    def _repr_fits_vertical_(self) -> bool:
         """
         Check length against max_rows.
         """
         max_rows = get_option("display.max_rows")
         return len(self) <= max_rows
 
-    def _repr_fits_horizontal_(self, ignore_width=False):
+    def _repr_fits_horizontal_(self, ignore_width: bool = False) -> bool:
         """
         Check if full repr fits in horizontal boundaries imposed by the display
         options width and max_columns.
@@ -620,7 +620,7 @@ def _repr_fits_horizontal_(self, ignore_width=False):
 
         return repr_width < width
 
-    def _info_repr(self):
+    def _info_repr(self) -> bool:
         """
         True if the repr should show the info view.
         """
@@ -629,7 +629,7 @@ def _info_repr(self):
             self._repr_fits_horizontal_() and self._repr_fits_vertical_()
         )
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         """
         Return a string representation for a particular DataFrame.
         """
@@ -659,7 +659,7 @@ def __repr__(self):
 
         return buf.getvalue()
 
-    def _repr_html_(self):
+    def _repr_html_(self) -> Optional[str]:
         """
         Return a html representation for a particular DataFrame.
 
@@ -706,6 +706,7 @@ def _repr_html_(self):
             return None
 
     @Substitution(
+        header_type="bool or sequence",
         header="Write out the column names. If a list of strings "
         "is given, it is assumed to be aliases for the "
         "column names",
@@ -715,25 +716,25 @@ def _repr_html_(self):
     @Substitution(shared_params=fmt.common_docstring, returns=fmt.return_docstring)
     def to_string(
         self,
-        buf=None,
-        columns=None,
-        col_space=None,
-        header=True,
-        index=True,
-        na_rep="NaN",
-        formatters=None,
-        float_format=None,
-        sparsify=None,
-        index_names=True,
-        justify=None,
-        max_rows=None,
-        min_rows=None,
-        max_cols=None,
-        show_dimensions=False,
-        decimal=".",
-        line_width=None,
-        max_colwidth=None,
-    ):
+        buf: Optional[FilePathOrBuffer[str]] = None,
+        columns: Optional[Sequence[str]] = None,
+        col_space: Optional[int] = None,
+        header: Union[bool, Sequence[str]] = True,
+        index: bool = True,
+        na_rep: str = "NaN",
+        formatters: Optional[fmt.formatters_type] = None,
+        float_format: Optional[fmt.float_format_type] = None,
+        sparsify: Optional[bool] = None,
+        index_names: bool = True,
+        justify: Optional[str] = None,
+        max_rows: Optional[int] = None,
+        min_rows: Optional[int] = None,
+        max_cols: Optional[int] = None,
+        show_dimensions: bool = False,
+        decimal: str = ".",
+        line_width: Optional[int] = None,
+        max_colwidth: Optional[int] = None,
+    ) -> Optional[str]:
         """
         Render a DataFrame to a console-friendly tabular output.
         %(shared_params)s
@@ -2234,6 +2235,7 @@ def to_parquet(
         )
 
     @Substitution(
+        header_type="bool",
         header="Whether to print column labels, default True",
         col_space_type="str or int",
         col_space="The minimum width of each column in CSS length "
diff --git a/pandas/io/formats/format.py b/pandas/io/formats/format.py
index 4a66ad48d1318..e7a7b34100a23 100644
--- a/pandas/io/formats/format.py
+++ b/pandas/io/formats/format.py
@@ -21,6 +21,7 @@
     Iterable,
     List,
     Optional,
+    Sequence,
     Tuple,
     Type,
     Union,
@@ -90,7 +91,7 @@
             The subset of columns to write. Writes all columns by default.
         col_space : %(col_space_type)s, optional
             %(col_space)s.
-        header : bool, optional
+        header : %(header_type)s, optional
             %(header)s.
         index : bool, optional, default True
             Whether to print index (row) labels.
@@ -530,9 +531,9 @@ class DataFrameFormatter(TableFormatter):
     def __init__(
         self,
         frame: "DataFrame",
-        columns: Optional[List[str]] = None,
+        columns: Optional[Sequence[str]] = None,
         col_space: Optional[Union[str, int]] = None,
-        header: Union[bool, List[str]] = True,
+        header: Union[bool, Sequence[str]] = True,
         index: bool = True,
         na_rep: str = "NaN",
         formatters: Optional[formatters_type] = None,