A021684 - OEIS

A021684

Expansion of 1/((1-x)*(1-3*x)*(1-9*x)*(1-10*x)).

1, 23, 360, 4810, 59111, 690573, 7801990, 86089520, 933531621, 9989073523, 105774639620, 1110701801430, 11583617458531, 120125571974873, 1239860303429250, 12746044308940540, 130587414625807841, 1334016890279410623, 13593453599567226880, 138214098268373746850

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OFFSET

0,2

COMMENTS

a(n) is the number of partitions of n into parts 1, 3, 9, and 10. - Joerg Arndt, Sep 29 2025

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (23,-169,417,-270).

FORMULA

a(n) = -1/144 + 10^(n+3)/63 + 3^(n+2)/28 - 3*9^(n+2)/16. - R. J. Mathar, Mar 15 2011

MATHEMATICA

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)

LinearRecurrence[{23, -169, 417, -270}, {1, 23, 360, 4810}, 30] (* Harvey P. Dale, Nov 18 2018 *)

PROG

(PARI) Vec(1/((1-x)*(1-3*x)*(1-9*x)*(1-10*x))+O(x^30)) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Sequence in context: A020346 A025964 A180361 * A138578 A077515 A025942

Adjacent sequences: A021681 A021682 A021683 * A021685 A021686 A021687

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved