A191899 Number of compositions of odd natural numbers into 8 parts <=n.

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

Offset: 0

Author

Adi Dani, Jun 19 2011

Keywords

• nonn
• easy

Examples

			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
		

Links

• Adi Dani, Restricted compositions of natural numbers
• Index entries for linear recurrences with constant coefficients, signature (8,-27,48,-42,0,42,-48,27,-8,1).

Programs

Mathematica

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 *)

PARI

a(n)=1/2*((n+1)^8-(1+(-1)^n)/2) \\ Charles R Greathouse IV, Jul 06 2017

Formula

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