A092534 Expansion of (1-x+x^2)*(1+x^4)/((1-x)^2*(1-x^2)).

1, 1, 3, 4, 8, 10, 16, 20, 28, 34, 44, 52, 64, 74, 88, 100, 116, 130, 148, 164, 184, 202, 224, 244, 268, 290, 316, 340, 368, 394, 424, 452, 484, 514, 548, 580, 616, 650, 688, 724, 764, 802, 844, 884, 928, 970, 1016, 1060, 1108, 1154, 1204, 1252, 1304, 1354, 1408, 1460

Offset

0,3

Comments

At one time this was given as the g.f. for A004657. In fact it produces a different sequence, showm here.

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

The g.f. can also be written as (1+x^2+x^4)*(1+x^4)/((1-x)*(1-x^2)*(1-x^3)). - N. J. A. Sloane, Nov 07 2017

From Colin Barker, Apr 14 2016: (Start)

a(n) = (13+3*(-1)^n-4*n+2*n^2)/4 for n>2.

a(n) = (n^2-2*n+8)/2 for n>2 and even.

a(n) = (n^2-2*n+5)/2 for n>2 and odd.

a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6) for n>6.

(End)

Mathematica

CoefficientList[Series[(1+x^2+x^4)(1+x^4)/((1-x)(1-x^2)(1-x^3)), {x, 0, 60}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {1, 1, 3, 4, 8, 10, 16}, 60] (* Harvey P. Dale, Nov 07 2017 *)

Prog

(PARI) Vec((1+x^2+x^4)*(1+x^4)/((1-x)*(1-x^2)*(1-x^3)) + O(x^50)) \\ Colin Barker, Apr 14 2016

Crossrefs

Sequence in context: A043306 A308844 A131355 * A005232 A165272 A310010

Adjacent sequences: A092531 A092532 A092533 * A092535 A092536 A092537

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 08 2004

Extensions

Definition simplified by N. J. A. Sloane, Nov 07 2017

Status

approved