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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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

Adjacent sequences:  A191899 A191900 A191901 * A191903 A191904 A191905

KEYWORD

nonn,easy

AUTHOR

Adi Dani, Jun 19 2011

STATUS

approved

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Last modified June 19 11:31 EDT 2019. Contains 324219 sequences. (Running on oeis4.)