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A191902
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Number of compositions of odd positive integers into 5 parts <= n.
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2
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0, 16, 121, 512, 1562, 3888, 8403, 16384, 29524, 50000, 80525, 124416, 185646, 268912, 379687, 524288, 709928, 944784, 1238049, 1600000, 2042050, 2576816, 3218171, 3981312, 4882812, 5940688, 7174453, 8605184, 10255574, 12150000, 14314575
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = ((n + 1)^5 - (1 + (-1)^n)/2)/2.
G.f.: x*(16 + 41*x + 51*x^2 + 11*x^3 + x^4) / ( (1+x)*(x-1)^6 ). (End)
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EXAMPLE
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a(1)=16: the 16 compositions of odd numbers into 5 parts <= 1 are
1: (0,0,0,0,1) --> 5!/(4!1!) = 5;
3: (0,0,1,1,1) --> 5!/(2!3!) = 10;
5: (1,1,1,1,1) --> 5!/(0!5!) = 1.
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MATHEMATICA
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Table[Floor[1/2*((n + 1)^5 - (1 + (-1)^n)/2)], {n, 0, 30}]
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PROG
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(Magma) [((n + 1)^5 - (1 + (-1)^n)/2)/2: n in [0..50]]; // Vincenzo Librandi, Jul 04 2011
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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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