A322039 Expansion of (1 + x)^2 / ((1 - x)^2*(1 + 2*x)^2).

1, 0, 4, -4, 16, -28, 72, -148, 336, -716, 1560, -3332, 7136, -15164, 32168, -67956, 143216, -300972, 631096, -1320420, 2757376, -5747740, 11961544, -24855124, 51574416, -106877068, 221210712, -457334468, 944495136, -1948642556

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 (-2,3,4,-4).

Crossrefs

Cf. A322038, A322040.

Programs

Mathematica

LinearRecurrence[{-2, 3, 4, -4}, {1, 0, 4, -4}, 100] (* Amiram Eldar, Dec 04 2018 *)

PARI

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

Formula

From Colin Barker, Dec 04 2018: (Start)

a(n) = -2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4) for n>3.

a(n) = (16 + 11*(-2)^n + 3*(4+(-2)^n)*n) / 27.

(End)