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A191899 Number of compositions of odd natural numbers into 8 parts <=n 0
0, 128, 3280, 32768, 195312, 839808, 2882400, 8388608, 21523360, 50000000, 107179440, 214990848, 407865360, 737894528, 1281445312, 2147483648, 3487878720, 5509980288, 8491781520, 12800000000, 18911429680, 27437936768, 39155492640, 55037657088, 76293945312, 104413532288 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

Adi Dani, Restricted compositions of natural numbers

Index entries for linear recurrences with constant coefficients, signature (8,-27,48,-42,0,42,-48,27,-8,1).

FORMULA

a(n) = 1/2*((n + 1)^8 - (1 + (-1)^n)/2).

G.f.: -16*x*(8*x^6+141*x^5+624*x^4+974*x^3+624*x^2+141*x+8) / ((x-1)^9*(x+1)). - Colin Barker, May 16 2013

EXAMPLE

a(1)=128 compositions of odd numbers into 8 parts <=1

1:(0,0,0,0,0,0,0,1)-->8!/(7!1!)= 8

3:(0,0,0,0,0,1,1,1)-->8!/(5!3!)=56

5:(0,0,0,1,1,1,1,1)-->8!/(3!5!)=56

7:(0,1,1,1,1,1,1,1)-->8!/(1!7!)= 8

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

                               128

MATHEMATICA

Table[Floor[1/2*((n + 1)^8 - (1 + (-1)^n)/2)], {n, 0, 25}]

LinearRecurrence[{8, -27, 48, -42, 0, 42, -48, 27, -8, 1}, {0, 128, 3280, 32768, 195312, 839808, 2882400, 8388608, 21523360, 50000000}, 30] (* Harvey P. Dale, Aug 30 2016 *)

PROG

(PARI) a(n)=1/2*((n+1)^8-(1+(-1)^n)/2) \\ Charles R Greathouse IV, Jul 06 2017

CROSSREFS

Sequence in context: A264383 A022150 A269001 * A191495 A250172 A188303

Adjacent sequences:  A191896 A191897 A191898 * A191900 A191901 A191902

KEYWORD

nonn,easy

AUTHOR

Adi Dani, Jun 19 2011

STATUS

approved

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Last modified May 25 11:17 EDT 2019. Contains 323539 sequences. (Running on oeis4.)