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A191901
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Number of compositions of odd natural numbers into 6 parts <= n.
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1
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0, 32, 364, 2048, 7812, 23328, 58824, 131072, 265720, 500000, 885780, 1492992, 2413404, 3764768, 5695312, 8388608, 12068784, 17006112, 23522940, 32000000, 42883060, 56689952, 74017944, 95551488, 122070312, 154457888, 193710244, 240945152, 297411660, 364500000, 443751840
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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)^6 - (1 + (-1)^n)/2)/2.
G.f. -4*x*(8+43*x+78*x^2+43*x^3+8*x^4) / ( (1+x)*(x-1)^7 ). - R. J. Mathar, Jun 26 2011
a(0)=0, a(1)=32, a(2)=364, a(3)=2048, a(4)=7812, a(5)=23328, a(6)=58824, a(7)=131072, a(n)=6*a(n-1)-14*a(n-2)+14*a(n-3)-14*a(n-5)+ 14*a(n-6)- 6*a(n-7)+a(n-8). - Harvey P. Dale, Apr 12 2015
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EXAMPLE
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a(1)=32 compositions of odd numbers into 6 parts <=1.
1:(0,0,0,0,0,1)-->6!/(5!1!)= 6
3:(0,0,0,1,1,1)-->6!/(3!3!)=20
5:(0,1,1,1,1,1)-->6!/(1!5!)= 6
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32
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MAPLE
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MATHEMATICA
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Table[Floor[1/2*((n + 1)^6 - (1 + (-1)^n)/2)], {n, 0, 30}]
LinearRecurrence[{6, -14, 14, 0, -14, 14, -6, 1}, {0, 32, 364, 2048, 7812, 23328, 58824, 131072}, 40] (* Harvey P. Dale, Apr 12 2015 *)
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PROG
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(Magma) [((n + 1)^6 - (1 + (-1)^n)/2)/2 : n in [0..25]]; // Vincenzo Librandi, Jul 03 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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