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 A132750 A132749 * [1, 2, 3, ...] = A007318 * A065190. 5
 1, 4, 9, 21, 49, 113, 257, 577, 1281, 2817, 6145, 13313, 28673, 61441, 131073, 278529, 589825, 1245185, 2621441, 5505025, 11534337, 24117249, 50331649, 104857601, 218103809, 452984833, 939524097, 1946157057, 4026531841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equals double binomial transform of [1, 2, -3, 7, -15, 31, -63, 127, -255, ...]. - Gary W. Adamson, Jul 23 2008 For n >= 1, also the number of cliques in the n-hypercube graph Q_n. - Eric W. Weisstein, Mar 31 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 V. Jelinek, T. Mansour, M. Shattuck, On multiple pattern avoiding set partitions, Adv. Appl. Math. 50 (2) (2013) 292-326, Lemma 4.21 (sequence starting 1, 1, 2, 4, 9, 21, .... with offset 0) Eric Weisstein's World of Mathematics, Clique Eric Weisstein's World of Mathematics, Hypercube Graph Index entries for linear recurrences with constant coefficients, signature (5,-8,4). FORMULA A132749 as an infinite lower triangular matrix * vector [1, 2, 3, ...]. Binomial transform of A065190 (with an incorrect offset) Row sums of triangle A135224. - Gary W. Adamson, Nov 23 2007 Empirical G.f.: (1-x-3*x^2+4*x^3)/((1-x)*(1-2*x)^2). - Colin Barker, Aug 09 2012 a(n) = n*2^(n-1) + 2^n + 1 - 0^n. - Tim Smith, Sep 25 2014 a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). - Wesley Ivan Hurt, Sep 26 2014 EXAMPLE a(3) = 21 = (1, 3, 3, 1) dot (1, 3, 2, 5) = (1 + 9 + 6 + 5) = 21; where A065190 = (1, 3, 2, 5, 4, 7, 6, 9, ...). MAPLE A132750:=n->n*2^(n-1)+2^n+1-0^n: seq(A132750(n), n=0..30); # Wesley Ivan Hurt, Sep 26 2014 MATHEMATICA Join[{1}, Table[n*2^(n - 1) + 2^n + 1, {n, 30}]] (* Wesley Ivan Hurt, Sep 26 2014 *) Join[{1}, LinearRecurrence[{5, -8, 4}, {4, 9, 21}, 30]] (* Vincenzo Librandi, Apr 01 2017 *) PROG (MAGMA) [n*2^(n - 1) + 2^n + 1 - 0^n : n in [0..30]]; // Wesley Ivan Hurt, Sep 26 2014 CROSSREFS Cf. A132749, A065190. Cf. A135224. Sequence in context: A103040 A084861 A122498 * A297296 A048582 A069231 Adjacent sequences:  A132747 A132748 A132749 * A132751 A132752 A132753 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Aug 28 2007 STATUS approved

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Last modified October 21 07:05 EDT 2019. Contains 328292 sequences. (Running on oeis4.)