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A191900
Number of compositions of odd natural numbers into 7 parts <=n
0
0, 64, 1093, 8192, 39062, 139968, 411771, 1048576, 2391484, 5000000, 9743585, 17915904, 31374258, 52706752, 85429687, 134217728, 205169336, 306110016, 446935869, 640000000, 900544270, 1247178944, 1702412723, 2293235712, 3051757812, 4015905088
OFFSET
0,2
FORMULA
a(n) = ((n + 1)^7 - (1 + (-1)^n)/2)/2.
a(2*n+1) = A191494(2*n+1); a(2*n) = A191494(2*n)-1.
G.f.: x*(64+645*x+1821*x^2+1786*x^3+666*x^4+57*x^5+x^6) / ( (1+x)*(x-1)^8 ). - R. J. Mathar, Jun 22 2011
EXAMPLE
a(1)=64: the 64 compositions of odd numbers into 7 parts <=1
1:(0,0,0,0,0,0,1)-->7!/(6!1!)= 7
3:(0,0,0,0,1,1,1)-->7!/(4!3!)=35
5:(0,0,1,1,1,1,1)-->7!/(2!5!)=21
7:(1,1,1,1,1,1,1)-->7!/(0!7!)= 1.
MATHEMATICA
Table[Floor[1/2*((n + 1)^7 - (1 + (-1)^n)/2)], {n, 0, 25}]
PROG
(PARI) a(n)=((n+1)^7-(1+(-1)^n)/2)/2 \\ Charles R Greathouse IV, Jul 06 2017
CROSSREFS
Sequence in context: A300880 A301490 A223070 * A191494 A269000 A189276
KEYWORD
nonn,easy
AUTHOR
Adi Dani, Jun 19 2011
STATUS
approved