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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Adi Dani, Restricted compositions of natural numbers. Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1). 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 Cf. A011863, A171714. Sequence in context: A105374 A162668 A227733 * A028596 A264602 A125198 Adjacent sequences: A191900 A191901 A191902 * A191904 A191905 A191906 KEYWORD nonn,easy AUTHOR Adi Dani, Jun 19 2011 STATUS approved

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Last modified November 27 05:12 EST 2022. Contains 358362 sequences. (Running on oeis4.)