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A191680 Number of compositions of odd natural numbers into 9 parts <= n. 1
0, 256, 9841, 131072, 976562, 5038848, 20176803, 67108864, 193710244, 500000000, 1178973845, 2579890176, 5302249686, 10330523392, 19221679687, 34359738368, 59293938248, 99179645184, 161343848889, 256000000000, 397140023290, 603634608896, 900576330731, 1320903770112, 1907348632812, 2714751839488 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Adi Dani, Restricted compositions of natural numbers

FORMULA

a(n) = ((n + 1)^9 - (1 + (-1)^n)/2)/2.

G.f.: x*(256 + 7537*x + 51463*x^2 + 122149*x^3 + 122275*x^4 + 51379*x^5 + 7573*x^6 + 247*x^7 + x^8) / ( (1+x)*(x-1)^10 ). - R. J. Mathar, Jun 29 2011

a(n) = 9*a(n-1) - 35*a(n-2) + 75*a(n-3) - 90*a(n-4) + 42*a(n-5) + 42*a(n-6) - 90*a(n-7) + 75*a(n-8) - 35*a(n-9) + 9*a(n-10) - a(n-11). - R. J. Mathar, Jun 29 2011

a(2n) = A191496(2n) - 1. a(2n+1) = A191496(2n+1). - R. J. Mathar, Jun 29 2011

EXAMPLE

a(1)=256 compositions of odd numbers into 9 parts <= 1:

  1: (0,0,0,0,0,0,0,0,1) --> 9!/(8!1!) =   9

  3: (0,0,0,0,0,0,1,1,1) --> 9!/(6!3!) =  84

  5: (0,0,0,0,1,1,1,1,1) --> 9!/(4!5!) = 126

  7: (0,0,1,1,1,1,1,1,1) --> 9!/(2!7!) =  36

  9: (1,1,1,1,1,1,1,1,1) --> 9!/(0!9!) =   1

  ------------------------------------------

                                         256

MATHEMATICA

Table[Floor[1/2*((n + 1)^9 - (1 + (-1)^n)/2)], {n, 0, 25}]

PROG

(MAGMA) [1/2*((n + 1)^9 - (1 + (-1)^n)/2): n in [0..30]]; // Vincenzo Librandi, Jun 16 2011

CROSSREFS

Sequence in context: A253135 A128991 A230973 * A191496 A016960 A224393

Adjacent sequences:  A191677 A191678 A191679 * A191681 A191682 A191683

KEYWORD

nonn

AUTHOR

Adi Dani, Jun 11 2011

EXTENSIONS

Offset changed from 1 to 0 by Vincenzo Librandi, Jun 16 2011

STATUS

approved

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Last modified September 19 04:39 EDT 2019. Contains 327187 sequences. (Running on oeis4.)