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A191899
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Number of compositions of odd natural numbers into 8 parts <=n
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0
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0, 128, 3280, 32768, 195312, 839808, 2882400, 8388608, 21523360, 50000000, 107179440, 214990848, 407865360, 737894528, 1281445312, 2147483648, 3487878720, 5509980288, 8491781520, 12800000000, 18911429680, 27437936768, 39155492640, 55037657088, 76293945312, 104413532288
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (8,-27,48,-42,0,42,-48,27,-8,1).
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FORMULA
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a(n) = 1/2*((n + 1)^8 - (1 + (-1)^n)/2).
G.f.: -16*x*(8*x^6+141*x^5+624*x^4+974*x^3+624*x^2+141*x+8) / ((x-1)^9*(x+1)). - Colin Barker, May 16 2013
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EXAMPLE
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a(1)=128 compositions of odd numbers into 8 parts <=1
1:(0,0,0,0,0,0,0,1)-->8!/(7!1!)= 8
3:(0,0,0,0,0,1,1,1)-->8!/(5!3!)=56
5:(0,0,0,1,1,1,1,1)-->8!/(3!5!)=56
7:(0,1,1,1,1,1,1,1)-->8!/(1!7!)= 8
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128
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MATHEMATICA
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Table[Floor[1/2*((n + 1)^8 - (1 + (-1)^n)/2)], {n, 0, 25}]
LinearRecurrence[{8, -27, 48, -42, 0, 42, -48, 27, -8, 1}, {0, 128, 3280, 32768, 195312, 839808, 2882400, 8388608, 21523360, 50000000}, 30] (* Harvey P. Dale, Aug 30 2016 *)
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PROG
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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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