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A029074
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Expansion of 1/((1-x)(1-x^4)(1-x^7)(1-x^9)).
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1
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1, 1, 1, 1, 2, 2, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 20, 22, 24, 26, 29, 31, 34, 37, 40, 43, 46, 50, 53, 57, 61, 66, 70, 74, 79, 84, 89, 94, 100, 106, 112, 118, 124, 131, 138, 145, 152, 160, 168, 176
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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 1, 4, 7 and 9. - Ilya Gutkovskiy, May 18 2017
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1,0,1,-1,1,-1,-1,1,-1,1,0,-1,1,0,0,1,-1).
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FORMULA
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a(n) = a(n-1) + a(n-4) - a(n-5) + a(n-7) - a(n-8) + a(n-9) - a(n-10) - a(n-11) + a(n-12) - a(n-13) + a(n-14) - a(n-16) + a(n-17) + a(n-20) - a(n-21), n > 20.
Lim_{n->infinity} a(n)/a(n+1) = 1.
(End)
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MATHEMATICA
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CoefficientList[Series[1/((1-x)(1-x^4)(1-x^7)(1-x^9)), {x, 0, 60}], x] (* Harvey P. Dale, Aug 19 2014 *)
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PROG
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(PARI) first(n) = Vec(1/((1-x)*(1-x^4)*(1-x^7)*(1-x^9)) + O(x^n)) \\ Iain Fox, Nov 30 2017
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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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