OFFSET
0,19
COMMENTS
a(n) is the number of partitions of n into parts 5, 8, and 9. - 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 (0,0,0,0,1,0,0,1,1,0,0,0,-1,-1,0,0,-1,0,0,0,0,1).
FORMULA
a(n) = a(n-5) + a(n-8) + a(n-9) - a(n-13) - a(n-14) - a(n-17) + a(n-22). - G. C. Greubel, Nov 19 2022
From Hoang Xuan Thanh, Sep 19 2025: (Start)
a(n) = floor((n-2)*(n+24)/720 + ((n^2+2*n+2) mod 5)/5 + ((n^2+4*n+6) mod 9)/9).
a(n) = floor((5*n^2+14*n+16)/16) - floor((n^2+2*n+2)/5) - floor((n^2+4*n+6)/9). (End)
MATHEMATICA
CoefficientList[Series[1/((1-x^5)(1-x^8)(1-x^9)), {x, 0, 80}], x] (* G. C. Greubel, Nov 19 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 80); Coefficients(R!( 1/((1-x^5)*(1-x^8)*(1-x^9)) )); // G. C. Greubel, Nov 19 2022
(SageMath)
def A025887_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x^5)*(1-x^8)*(1-x^9)) ).list()
A025887_list(80) # G. C. Greubel, Nov 19 2022
(PARI) Vec(1/((1-x^5)*(1-x^8)*(1-x^9))+O(x^78)) \\ Stefano Spezia, Sep 17 2025
(PARI) a(n) = (n^2+22*n-408)/720 + [2, 0, 0, 2, 1][n%5+1]/5 + [6, 2, 0, 0, 2, 6, 3, 2, 3][n%9+1]/9 + [8, 5, 8, 1, 0, 5, 0, 1][n%8+1]/16 \\ Hoang Xuan Thanh, Sep 19 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved