A055104 Expansion of 1 + q/((1-q)*(1-q^2)) + q^2/((1-q)*(1-q^2)*(1-q^3)*(1-q^4)).

1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 20, 24, 29, 34, 41, 47, 55, 63, 73, 82, 94, 105, 119, 132, 148, 163, 182, 199, 220, 240, 264, 286, 313, 338, 368, 396, 429, 460, 497, 531, 571, 609, 653, 694, 742, 787, 839, 888, 944, 997, 1058, 1115, 1180, 1242

Offset

0,3

Comments

First 3 terms of a sum studied by Ramanujan.

Links

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

G. E. Andrews, Simplicity and surprise in Ramanujan's "Lost" Notebook, Amer. Math. Monthly, 104 (No. 10, Dec. 1997), 918-925.

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

Mathematica

LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 20}, 60] (* Harvey P. Dale, Mar 11 2019 *)

Prog

(PARI) Vec((1 - x^4 + x^5 - x^9 + x^10) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)) + O(x^100)) \\ Colin Barker, Oct 02 2017

Crossrefs

Sequence in context: A002984 A109965 A008669 * A062435 A171997 A020702

Adjacent sequences: A055101 A055102 A055103 * A055105 A055106 A055107

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 14 2000

Status

approved