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

Author

Yutong Li, Aug 11 2020

Keywords

• nonn
• easy

Examples

			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):
._______        _______
|_|_|   |      |_|_|   |
|   |___|      |_|_|___|
|___|   |      |   |   |
|_|_|___|      |_ _|___|
		

Links

• 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).

Crossrefs

Cf. A063443.

Programs

Mathematica

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

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)

Extensions

Edited by Greg Dresden, Aug 18 2020