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A191902
Number of compositions of odd positive integers into 5 parts <= n.
2
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
OFFSET
0,2
FORMULA
a(n) = ((n + 1)^5 - (1 + (-1)^n)/2)/2.
From R. J. Mathar, Jun 22 2011: (Start)
a(2n+1) = A191484(2n+1); a(2n) = A191484(2n) - 1.
G.f.: x*(16 + 41*x + 51*x^2 + 11*x^3 + x^4) / ( (1+x)*(x-1)^6 ). (End)
EXAMPLE
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.
MATHEMATICA
Table[Floor[1/2*((n + 1)^5 - (1 + (-1)^n)/2)], {n, 0, 30}]
PROG
(Magma) [((n + 1)^5 - (1 + (-1)^n)/2)/2: n in [0..50]]; // Vincenzo Librandi, Jul 04 2011
(PARI) a(n)=((n+1)^5-(1+(-1)^n)/2)/2 \\ Charles R Greathouse IV, Jul 06 2017
CROSSREFS
Cf. A191484.
Sequence in context: A171584 A017030 A082921 * A294140 A014765 A081071
KEYWORD
nonn,easy
AUTHOR
Adi Dani, Jun 19 2011
STATUS
approved