A322040 Expansion of (1 + x)^2 / ((1 - x)^2*(1 + 2*x + 2*x^2)^2).

1, 0, 0, 4, -4, 4, 8, -20, 32, -12, -40, 124, -160, 68, 232, -628, 816, -300, -1160, 3100, -3904, 1380, 5640, -14676, 18256, -6156, -26472, 67900, -83488, 27268, 121640, -308276, 375920, -119532, -549448, 1379932, -1671424, 520100, 2449480

Offset: 0

Author

N. J. A. Sloane, Dec 03 2018

Keywords

• sign
• easy

Comments

Connected with tiling of torus by squares (see A322038).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,-1,4,4,0,-4).

Crossrefs

Cf. A322038, A322039.

Programs

Mathematica

LinearRecurrence[{-2, -1, 4, 4, 0, -4}, {1, 0, 0, 4, -4, 4}, 100] (* Amiram Eldar, Dec 04 2018 *)
CoefficientList[Series[(1+x)^2/((1-x)^2(1+2x+2x^2)^2),{x,0,40}],x] (* Harvey P. Dale, Jan 20 2021 *)

PARI

Vec((1 + x)^2 / ((1 - x)^2*(1 + 2*x + 2*x^2)^2) + O(x^40)) \\ Colin Barker, Dec 04 2018

Formula

a(n) = -2*a(n-1) - a(n-2) + 4*a(n-3) + 4*a(n-4) - 4*a(n-6) for n>5. - Colin Barker, Dec 04 2018