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 A217947 a(n) = (n+1)*(n^3+15*n^2+74*n+132)/12. 1
 11, 37, 87, 172, 305, 501, 777, 1152, 1647, 2285, 3091, 4092, 5317, 6797, 8565, 10656, 13107, 15957, 19247, 23020, 27321, 32197, 37697, 43872, 50775, 58461, 66987, 76412, 86797, 98205, 110701, 124352, 139227, 155397, 172935, 191916, 212417, 234517, 258297, 283840, 311231 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Ping Sun, Proof of two conjectures of Petkovsek and Wilf on Gessel walks Discrete Math. 312 (2012), no. 24, 3649--3655. MR2979494. See Th. 1.2, case 3. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: (11-18*x+12*x^2-3*x^3)/(1-x)^5. - Vincenzo Librandi, Dec 12 2014 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) n>4. - Vincenzo Librandi, Dec 12 2014 MATHEMATICA Table[(n + 1) (n^3 + 15 n^2 + 74 n + 132) / 12, {n, 0, 50}] (* or *) CoefficientList[Series[(11 - 18 x + 12 x^2 - 3 x^3) / (1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 12 2014 *) PROG (Maxima) A217947(n):=(n+1)*(n^3+15*n^2+74*n+132)/12\$ makelist(A217947(n), n, 0, 30); /* Martin Ettl, Nov 08 2012 */ (MAGMA) [(n+1)*(n^3+15*n^2+74*n+132)/12: n in [0..50]] /* or */ I:=[11, 37, 87, 172, 305]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..50]] ; // Vincenzo Librandi, Dec 12 2014 CROSSREFS Sequence in context: A188135 A188382 A090950 * A124479 A140373 A316191 Adjacent sequences:  A217944 A217945 A217946 * A217948 A217949 A217950 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 07 2012 STATUS approved

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Last modified May 18 12:24 EDT 2021. Contains 343995 sequences. (Running on oeis4.)