A025888 - OEIS

A025888

Expansion of 1/((1-x^5)*(1-x^8)*(1-x^10)).

1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 6, 3, 2, 4, 3, 6, 4, 2, 6, 3, 8, 4, 3, 6, 4, 8, 6, 3, 8, 4, 10, 6, 4, 8, 6, 10, 8, 4, 10, 6, 12, 8, 6, 10, 8, 12, 10, 6, 12, 8, 15, 10, 8

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OFFSET

0,11

COMMENTS

a(n) is the number of partitions of n into parts 5, 8, and 10. - Joerg Arndt, Nov 20 2022

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n) = a(n-5) + a(n-8) + a(n-10) - a(n-13) - a(n-15) - a(n-18) + a(n-23). - G. C. Greubel, Nov 19 2022

a(n) = floor((n+10)*((floor(n/5) + floor((n+2)/5))/10 + floor(n/2)/40) - (41*n^2 + 360*n - 900)/800). - Hoang Xuan Thanh, Sep 20 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^5)(1-x^8)(1-x^10)), {x, 0, 100}], x] (* Harvey P. Dale, Jul 26 2011 *)

PROG

(Magma) R<x>:=PowerSeriesRing(Rationals(), 90); Coefficients(R!( 1/((1-x^5)*(1-x^8)*(1-x^10)) )); // G. C. Greubel, Nov 19 2022

(SageMath)

def A025888_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( 1/((1-x^5)*(1-x^8)*(1-x^10)) ).list()

A025888_list(90) # G. C. Greubel, Nov 19 2022

(PARI) a(n) = (n^2 + 87*n + 1170 + (n+10)*(5*(-1)^n - 16*((n%5)+((n+2)%5))))\800 \\ Hoang Xuan Thanh, Sep 20 2025

CROSSREFS

Cf. A025887, A025889, A025890.

Sequence in context: A346478 A346250 A084143 * A145708 A138532 A339445

Adjacent sequences: A025885 A025886 A025887 * A025889 A025890 A025891

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved