A337024 Number of ways to tile a 2n X 2n square with 1 X 1 white and n X n black squares.

16, 35, 60, 91, 128, 171, 220, 275, 336, 403, 476, 555, 640, 731, 828, 931, 1040, 1155, 1276, 1403, 1536, 1675, 1820, 1971, 2128, 2291, 2460, 2635, 2816, 3003, 3196, 3395, 3600, 3811, 4028, 4251, 4480, 4715, 4956, 5203

Offset

1,1

Links

Table of n, a(n) for n=1..40.

R. J. Mathar, Tiling n x m rectangles with 1 x 1 and s x s squares, arXiv:1609.03964 [math.CO], 2016, Section 4.1.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 3*n^2 + 10*n + 3.

From Stefano Spezia, Aug 18 2020: (Start)

O.g.f.: x*(16 - 13*x + 3*x^2)/(1 - x)^3.

E.g.f.: exp(x)*(3 + 13*x + 3*x^2) - 3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

Example

For example, here are two of the 35 ways to tile a 4 X 4 square with 1 X 1 and 2 X 2 squares (where we have dropped the colors):
._______        _______
|_|_|   |      |_|_|   |
|   |___|      |_|_|___|
|___|   |      |   |   |
|_|_|___|      |_ _|___|

Mathematica

Table[3 n^2 + 10 n + 3, {n, 50}] (* Wesley Ivan Hurt, Nov 07 2020 *)

Crossrefs

Cf. A063443.

Sequence in context: A294073 A086119 A105509 * A219316 A317818 A236463

Adjacent sequences: A337021 A337022 A337023 * A337025 A337026 A337027

Keyword

nonn,easy

Author

Yutong Li, Aug 11 2020

Extensions

Edited by Greg Dresden, Aug 18 2020

Status

approved