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 A270809 a(n) = n^3/3 - 7*n/3 + 4. 0
 4, 2, 2, 6, 16, 34, 62, 102, 156, 226, 314, 422, 552, 706, 886, 1094, 1332, 1602, 1906, 2246, 2624, 3042, 3502, 4006, 4556, 5154, 5802, 6502, 7256, 8066, 8934, 9862, 10852, 11906, 13026, 14214, 15472, 16802, 18206, 19686, 21244, 22882, 24602, 26406, 28296, 30274 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS M. Diepenbroek, M. Maus, A. Stoll, Pattern Avoidance in Reverse Double Lists, Preprint 2015. See Theorem 3.14. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA O.g.f.: (4 - 14*x + 18*x^2 - 6*x^3)/(1-x)^4. - Vincenzo Librandi, Apr 08 2016 E.g.f.: (12 - 6*x + 3*x^2 + x^3)*exp(x)/3. - Bruno Berselli, Apr 08 2016 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, Apr 08 2016 a(n) = 2*A105163(n) for n>0. - Bruno Berselli, Apr 08 2016 MATHEMATICA Table[n^3 / 3 - 7 n / 3 + 4, {n, 0, 50}] (* Vincenzo Librandi, Apr 08 2016 *) PROG (MAGMA) [n^3/3-7*n/3+4: n in [0..50]]; // Vincenzo Librandi, Apr 08 2016 (PARI) vector(50, n, n--; n^3/3-7*n/3+4) \\ Bruno Berselli, Apr 08 2016 (PARI) x='x+O('x^99); Vec((4-14*x+18*x^2-6*x^3)/(1-x)^4) \\ Altug Alkan, Apr 08 2016 (Sage) [n^3/3-7*n/3+4 for n in [0..50]] # Bruno Berselli, Apr 08 2016 CROSSREFS Cf. A105163. Sequence in context: A284692 A019834 A261557 * A087507 A020777 A153810 Adjacent sequences:  A270806 A270807 A270808 * A270810 A270811 A270812 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Apr 06 2016 STATUS approved

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Last modified March 25 01:17 EDT 2019. Contains 321450 sequences. (Running on oeis4.)