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A191903
Number of compositions of odd natural numbers into 4 parts <= n.
3
0, 8, 40, 128, 312, 648, 1200, 2048, 3280, 5000, 7320, 10368, 14280, 19208, 25312, 32768, 41760, 52488, 65160, 80000, 97240, 117128, 139920, 165888, 195312, 228488, 265720, 307328, 353640, 405000, 461760, 524288, 592960, 668168, 750312
OFFSET
0,2
FORMULA
a(n) = ((n + 1)^4 - (1 + (-1)^n)/2)/2.
From R. J. Mathar, Jun 22 2011: (Start)
G.f.: 8*x*(1+x+x^2) / ( (1+x)*(1-x)^5 ).
a(n) = 8*A011863(n+1). (End)
a(n) = floor((n+1)^4/2). - Wesley Ivan Hurt, Jun 14 2013
Sum_{n>=1} 1/a(n) = 3/4 + Pi^4/720 - tanh(Pi/2)*Pi/4. - Amiram Eldar, Aug 13 2022
EXAMPLE
a(1) = 8 compositions of odd numbers into 4 parts < 1.
1:(0,0,0,1),(0,0,1,1),(0,1,0,0),(1,0,0,0)
3:(0,1,1,1),(1,0,1,1),(1,1,0,1),(1,1,1,0)
MATHEMATICA
Table[Floor[1/2*((n + 1)^4 - (1 + (-1)^n)/2)], {n, 0, 30}]
PROG
(Magma) [((n + 1)^4 - (1 + (-1)^n)/2)/2: n in [0..50]]; // Vincenzo Librandi, Jul 04 2011
CROSSREFS
Sequence in context: A105374 A162668 A227733 * A028596 A264602 A125198
KEYWORD
nonn,easy
AUTHOR
Adi Dani, Jun 19 2011
STATUS
approved