cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A347636 Number of ways to tile an n X n square with 1 X 1 squares and (n-2) X 2 vertical or horizontal rectangles.

Original entry on oeis.org

193, 399, 783, 1601, 3283, 6947, 14897, 32607, 72175, 161649, 364611, 827555, 1885729, 4310639, 9874319, 22654881, 52032883, 119601123, 275058321, 632823743, 1456319215, 3352072913, 7716633443, 17765737443, 40904125825, 94182711375
Offset: 5

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Author

Greg Dresden and Osondu Ugochukwu, Sep 09 2021

Keywords

Examples

			Here are two of the 193 possible tilings for a 5 X 5 square (using 1 X 1 squares and 3 X 2 rectangles):
._________   ._________
|_|     |_|  |_|_|     |
|_|_ _ _|_|  |   |_ _ _|
|   |_|   |  |   |_|   |
|   |_|   |  |___|_|   |
|___|_|___|  |_|_|_|___|
		

Crossrefs

Cf. A335560 which is the same problem but with 1 X 1 squares and (n-1) X 1 rectangles, and A337024 which uses 1 X 1 squares and 2 X 2 squares.

Formula

a(n) = 2*A006130(n) + 12*F(n + 1) + 16*F(n - 1) - 31 for F(n) = A000045(n) the Fibonacci sequence.
a(n) = 3*a(n-1) + a(n-2) - 7*a(n-3) + a(n-4) + 3*a(n-5).
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