A279230 Expansion of 1/((1-x)^2*(1-2*x+2*x^2)).

1, 4, 9, 14, 15, 8, -7, -22, -21, 12, 77, 142, 143, 16, -239, -494, -493, 20, 1045, 2070, 2071, 24, -4071, -8166, -8165, 28, 16413, 32798, 32799, 32, -65503, -131038, -131037, 36, 262181, 524326, 524327, 40, -1048535, -2097110, -2097109, 44, 4194349, 8388654, 8388655

Offset

0,2

Comments

Partial sums of A077860.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-7,6,-2).

Formula

a(n) = 4*a(n-1) - 7*a(n-2) + 6*a(n-3) - 2*a(n-4) for n>3.

a(n) = 2*a(n-1) - 2*a(n-2) + n + 1, with a(-1) = a(-2) = 0.

a(n) = (3 - (1-i)^(1+n) - (1+i)^(1+n) + n) where i=sqrt(-1). - Colin Barker, Aug 04 2017

From Seiichi Manyama, Apr 07 2019: (Start)

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n+3,2*k+3).

a(n) = Sum_{i=0..n} Sum_{j=0..n-i} (-1)^j * binomial(i+1,j+1) * binomial(n-i+1,j+1). (End)

Prog

(PARI) Vec(1 / ((1 - x)^2*(1 - 2*x + 2*x^2)) + O(x^50)) \\ Colin Barker, Aug 04 2017
(PARI) {a(n) = sum(k=0, n\2, (-1)^k*binomial(n+3, 2*k+3))} \\ Seiichi Manyama, Apr 07 2019

Crossrefs

Cf. A001477, A045618, A077859, A077860, A279231.

Sequence in context: A264733 A102776 A140343 * A244037 A091880 A141560

Adjacent sequences: A279227 A279228 A279229 * A279231 A279232 A279233

Keyword

sign,easy

Author

Philippe Deléham, Dec 08 2016

Status

approved