A082290 Expansion of (1+x+x^2)/((1+x^2)*(1+x)^4*(1-x)^5).

1, 2, 6, 9, 19, 26, 46, 59, 94, 116, 172, 206, 290, 340, 460, 530, 695, 790, 1010, 1135, 1421, 1582, 1946, 2149, 2604, 2856, 3416, 3724, 4404, 4776, 5592, 6036, 7005, 7530, 8670, 9285, 10615, 11330, 12870, 13695, 15466, 16412, 18436, 19514, 21814, 23036

Offset

0,2

Links

Table of n, a(n) for n=0..45.

Index entries for two-way infinite sequences

Index entries for linear recurrences with constant coefficients, signature (1, 3, -3, -2, 2, -2, 2, 3, -3, -1, 1).

Formula

Euler transform of length 4 sequence [ 2, 3, -1, 1]. - Michael Somos, Feb 15 2006

G.f.: (1 + x + x^2) / ((1 + x^2) * (1 + x)^4 * (1 - x)^5).

a(n) = 3*a(n-2) - 2*a(n-4) - 2*a(n-6) + 3*a(n-8) - a(n-10) + 3.

a(n) = a(-9-n) for all n in Z.

a(2*n) = A070893(n+1). a(2*n + 1) = A082289(n+4).

a(n) = (6*n^4+108*n^3+666*n^2+1620*n+1251+(4*n^3+54*n^2+236*n+333)*(-1)^n-48*(-1)^((6*n-1+(-1)^n)/4))/1536. - Luce ETIENNE, Oct 23 2014

Example

G.f. = 1 + 2*x + 6*x^2 + 9*x^3 + 19*x^4 + 26*x^5 + 46*x^6 + 59*x^7 + ...

Mathematica

Table[(6 n^4 + 108 n^3 + 666 n^2 + 1620 n + 1251 + (4 n^3 + 54 n^2 + 236 n + 333) (-1)^n - 48 (-1)^((6 n - 1 + (-1)^n)/4))/1536, {n, 0, 50}] (* after Luce ETIENNE; or, by definition: *) CoefficientList[Series[(1 + x + x^2)/((1 + x^2)*(1 + x)^4*(1 - x)^5), {x, 0, 50}], x] (* Bruno Berselli, Oct 26 2014 *)

Prog

(PARI) {a(n) = if( n<-8, a(-9-n), polcoeff( (1 + x + x^2) / ((1 + x^2) *(1 + x)^4 * (1 - x)^5) + x * O(x^n), n))};
(Magma) [(6*n^4 +108*n^3 +666*n^2 +1620*n +1251 +(4*n^3 +54*n^2 +236*n +333)*(-1)^n -48*(-1)^Floor((6*n -1 +(-1)^n)/4))/1536: n in [0..50]]; // Vincenzo Librandi, Oct 23 2014

Crossrefs

Cf. A070893, A082289.

Sequence in context: A076738 A291100 A361271 * A325536 A182984 A301798

Adjacent sequences: A082287 A082288 A082289 * A082291 A082292 A082293

Keyword

nonn,easy

Author

Michael Somos, Apr 07 2003

Status

approved