A191902 Number of compositions of odd positive integers into 5 parts <= n.

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

Author

Adi Dani, Jun 19 2011

Keywords

• nonn
• easy

Examples

			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.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Adi Dani, Restricted compositions of natural numbers
• Index entries for linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1).

Crossrefs

Cf. A191484.

Programs

Magma

[((n + 1)^5 - (1 + (-1)^n)/2)/2: n in [0..50]]; // Vincenzo Librandi, Jul 04 2011

Mathematica

Table[Floor[1/2*((n + 1)^5 - (1 + (-1)^n)/2)], {n, 0, 30}]

PARI

a(n)=((n+1)^5-(1+(-1)^n)/2)/2 \\ Charles R Greathouse IV, Jul 06 2017

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)