The On-Line Encyclopedia of Integer Sequences (OEIS)

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A191902

Number of compositions of odd positive integers into 5 parts <= n.
(history; published version)

#23 by Charles R Greathouse IV at Thu Sep 08 08:45:57 EDT 2022

PROG

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

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#22 by Michel Marcus at Mon Oct 08 01:44:00 EDT 2018

STATUS

reviewed

approved

#21 by Wesley Ivan Hurt at Sun Oct 07 22:51:23 EDT 2018

STATUS

proposed

reviewed

#20 by Wesley Ivan Hurt at Sun Oct 07 22:51:05 EDT 2018

STATUS

editing

proposed

#19 by Wesley Ivan Hurt at Sun Oct 07 22:50:26 EDT 2018

FORMULA

From _R. J. Mathar, _, Jun 22 2011: (Start)

#18 by Wesley Ivan Hurt at Sun Oct 07 22:49:53 EDT 2018

CROSSREFS

Cf. A191484.

STATUS

proposed

editing

#17 by Jon E. Schoenfield at Sun Oct 07 22:40:32 EDT 2018

STATUS

editing

proposed

#16 by Jon E. Schoenfield at Sun Oct 07 22:40:29 EDT 2018

NAME

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

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. - R. J. Mathar, Jun 22 2011

G.f. : x*(16 + 41*x + 51*x^2 + 11*x^3 + x^4) / ( (1+x)*(x-1)^6 ). - R. J. Mathar, Jun 22 2011(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.

PROG

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

STATUS

approved

editing

#15 by Charles R Greathouse IV at Thu Jul 06 01:33:13 EDT 2017

STATUS

editing

approved

#14 by Charles R Greathouse IV at Thu Jul 06 01:33:09 EDT 2017

LINKS

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,5,5,-9,5,-1).

PROG

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

KEYWORD

nonn,easy

STATUS

approved

editing