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A029129
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Expansion of 1/((1-x)*(1-x^8)*(1-x^9)*(1-x^12)).
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1
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1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 7, 7, 8, 9, 9, 9, 11, 12, 13, 14, 15, 16, 17, 17, 19, 21, 22, 23, 26, 27, 28, 29, 31, 33, 35, 36, 39, 42, 43, 44, 48, 50, 52, 54, 57, 60, 63, 64, 68, 72, 74, 76, 81, 84
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OFFSET
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0,9
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COMMENTS
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Number of partitions of n into parts 1, 8, 9, and 12. - Joerg Arndt, Jul 04 2014
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 1, -1, 0, 0, 0, -1, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1).
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MAPLE
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# this requires Maple 17 or later
N:= 10000: # to get a(0) to a(N)
with(SignalProcessing):
A1:= Array(0..N, 1):
A8:=Array(0..N, i -> `if`(i mod 8 = 0, 1, 0)):
A9:=Array(0..N, i -> `if`(i mod 9 = 0, 1, 0)):
A12:= Array(0..N, i -> `if`(i mod 12 = 0, 1, 0)):
B:= Convolution(A1, A8)[1..N+1]:
B:= Convolution(B, A9)[1..N+1]:
B:= Convolution(B, A12)[1..N+1]:
A:= map(round, ArrayTools:-Reshape(B, 0..N)):
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MATHEMATICA
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CoefficientList[Series[1/((1-x)*(1-x^8)*(1-x^9)*(1-x^12)), {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 04 2014 *)
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PROG
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(Maxima) a(n):=floor((2*n^3+90*n^2+21*n+13023)/10368+(n+15)*(-1)^n/384 +((n+10)*(1-(-1)^n)/2+5)*((-1)^floor(n/2))/96 +(floor(n/3) -floor((n-1)/3))*(n+3)/108 +(floor((n+2)/9) +floor((n+1)/9) +floor(n/9))/3)$ makelist(a(n), n, 0, 10000); /* Tani Akinari, Jul 03 2014 */
(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-x^8)*(1-x^9)*(1-x^12)))); // Bruno Berselli, Jul 04 2014
(Sage) m = 70; L.<x> = PowerSeriesRing(ZZ, m); f = 1/((1-x)*(1-x^8)*(1-x^9)*(1-x^12)); print(f.coefficients()) # Bruno Berselli, Jul 04 2014
(PARI) Vec(1/((1-x)*(1-x^8)*(1-x^9)*(1-x^12)) + O(x^70)) \\ Michel Marcus, Jul 04 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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