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A029139
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Expansion of 1/((1-x^2)(1-x^3)(1-x^4)(1-x^9)).
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1
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1, 0, 1, 1, 2, 1, 3, 2, 4, 4, 5, 5, 8, 7, 9, 10, 12, 12, 16, 15, 19, 20, 23, 23, 29, 28, 33, 35, 39, 40, 47, 47, 53, 56, 61, 63, 72, 72, 80, 84, 91, 93, 104, 105, 115, 120, 128, 132, 145, 147, 158, 165, 175, 180, 195, 198, 212, 220, 232, 238, 256, 260, 276, 286, 300, 308
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OFFSET
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0,5
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COMMENTS
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Number of partitions of n into parts 2, 3, 4, and 9. - Joerg Arndt, Aug 14 2013
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,-1,-1,-1,0,2,0,-1,-1,-1,1,1,1,0,-1).
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FORMULA
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a(n) = floor((2*n^3 + 54*n^2 + 431*n + 2247 + 81*(n+9)*(-1)^n + 192*cos(2*Pi*n/3)*(floor(n/3)+1))/2592). - Tani Akinari, Aug 13 2013
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MATHEMATICA
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CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^4)(1-x^9)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 18 2020 *)
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PROG
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(PARI) Vec( 1/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^9)) + O(x^66) ) \\ Joerg Arndt, Aug 14 2013
(PARI) a(n)=round((2*n^3+54*n^2+399*n+899)/2592+(n%3==0)*n/27+(n+9)*(-1)^n/32) \\ Tani Akinari, Jun 03 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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