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A191901 Number of compositions of odd natural numbers into 6 parts <= n. 1
0, 32, 364, 2048, 7812, 23328, 58824, 131072, 265720, 500000, 885780, 1492992, 2413404, 3764768, 5695312, 8388608, 12068784, 17006112, 23522940, 32000000, 42883060, 56689952, 74017944, 95551488, 122070312, 154457888, 193710244, 240945152, 297411660, 364500000, 443751840 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = ((n + 1)^6 - (1 + (-1)^n)/2)/2.
G.f. -4*x*(8+43*x+78*x^2+43*x^3+8*x^4) / ( (1+x)*(x-1)^7 ). - R. J. Mathar, Jun 26 2011
a(0)=0, a(1)=32, a(2)=364, a(3)=2048, a(4)=7812, a(5)=23328, a(6)=58824, a(7)=131072, a(n)=6*a(n-1)-14*a(n-2)+14*a(n-3)-14*a(n-5)+ 14*a(n-6)- 6*a(n-7)+a(n-8). - Harvey P. Dale, Apr 12 2015
EXAMPLE
a(1)=32 compositions of odd numbers into 6 parts <=1.
1:(0,0,0,0,0,1)-->6!/(5!1!)= 6
3:(0,0,0,1,1,1)-->6!/(3!3!)=20
5:(0,1,1,1,1,1)-->6!/(1!5!)= 6
-------------------------------------
32
MAPLE
A191901:=n->((n + 1)^6 - (1 + (-1)^n)/2)/2: seq(A191901(n), n=0..50); # Wesley Ivan Hurt, Apr 10 2017
MATHEMATICA
Table[Floor[1/2*((n + 1)^6 - (1 + (-1)^n)/2)], {n, 0, 30}]
LinearRecurrence[{6, -14, 14, 0, -14, 14, -6, 1}, {0, 32, 364, 2048, 7812, 23328, 58824, 131072}, 40] (* Harvey P. Dale, Apr 12 2015 *)
PROG
(Magma) [((n + 1)^6 - (1 + (-1)^n)/2)/2 : n in [0..25]]; // Vincenzo Librandi, Jul 03 2011
CROSSREFS
Sequence in context: A302818 A303511 A240787 * A191489 A055752 A362234
KEYWORD
nonn,easy
AUTHOR
Adi Dani, Jun 19 2011
STATUS
approved

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Last modified February 26 17:57 EST 2024. Contains 370352 sequences. (Running on oeis4.)