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A025897
Expansion of 1/((1-x^6)*(1-x^7)*(1-x^8)).
7
1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 5, 4, 5, 4, 5, 4, 6, 5, 6, 5, 6, 5, 7, 6, 8, 6, 7, 6, 8, 7, 9, 8, 9, 7, 9, 8, 10, 9, 11, 9, 11, 9, 11, 10, 12, 11
OFFSET
0,15
COMMENTS
a(n) is the number of partitions of n into parts 6, 7, and 8. - Joerg Arndt, Jan 22 2024
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,0,0,0,0,0,1).
FORMULA
a(n) = a(n-6) + a(n-7) + a(n-8) - a(n-13) - a(n-14) - a(n-15) + a(n-21). - Harvey P. Dale, Aug 17 2014
MATHEMATICA
CoefficientList[Series[1/((1-x^6)(1-x^7)(1-x^8)), {x, 0, 100}], x] (* Harvey P. Dale, Aug 17 2014 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^6)*(1-x^7)*(1-x^8)) )); // G. C. Greubel, Jan 22 2024
(SageMath)
def A025897_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x^6)*(1-x^7)*(1-x^8))).list()
A025897_list(100) # G. C. Greubel, Jan 22 2024
KEYWORD
nonn
STATUS
approved