OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (8,-27,48,-42,0,42,-48,27,-8,1).
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
EXAMPLE
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
-------------------------------------
128
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 *)
PROG
(PARI) a(n)=1/2*((n+1)^8-(1+(-1)^n)/2) \\ Charles R Greathouse IV, Jul 06 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Adi Dani, Jun 19 2011
STATUS
approved