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 A141015 a(0) = 0, a(1) = 1, a(2) = 2; for n > 2, a(n) = a(n-1) + 2*a(n-2) + a(n-3). 8
 0, 1, 2, 4, 9, 19, 41, 88, 189, 406, 872, 1873, 4023, 8641, 18560, 39865, 85626, 183916, 395033, 848491, 1822473, 3914488, 8407925, 18059374, 38789712, 83316385, 178955183, 384377665, 825604416, 1773314929, 3808901426 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Central axis of triangle G(n, k): G(n,0) = G(n+1, n+1) = 1, G(n+2, n+1) = 2, G(n+3, n+1) = 4, G(n+4, k) = G(n+1, k-1) + G(n+1, k) + G(n+2, k) + G(n+3, k) for k = 1..(n+1). (This is triangular array A140997.) Central axis of triangle G(n, k): G(n, n) = G(n+1, 0) = 1, G(n+2, 1) = 2, G(n+3, 2) = 4, G(n+4, k) = G(n+1, k-2) + G(n+1, k-3) + G(n+2, k-2) + G(n+3, k-1) for k = 3..(n+3). (This is triangular array A140994, which is a mirror image of A140997.) a(n-1) is the top left entry of the n-th power of any of the 3X3 matrices [0, 1, 1; 1, 1, 1; 0, 1, 0], [0, 1, 0; 1, 1, 1; 1, 1, 0], [0, 1, 1; 0, 0, 1; 1, 1, 1] or [0, 0, 1; 1, 0, 1; 1, 1, 1]. - R. J. Mathar, Feb 03 2014 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,2,1). FORMULA From R. J. Mathar, Aug 22 2008: (Start) O.g.f.: x*(1 + x)/(1 - x - 2*x^2 - x^3). a(n) = (-1)^(n+1)*A078039(n-1). (End) MATHEMATICA CoefficientList[Series[x (1 + x)/(1 - x - 2 x^2 - x^3), {x, 0, 50}], x] (* G. C. Greubel, Jun 09 2017 *) PROG (Sage) from sage.combinat.sloane_functions import recur_gen3; it = recur_gen3(0, 1, 2, 1, 2, 1); [it.next() for i in range(31)] # Zerinvary Lajos, May 17 2009 (PARI) x='x+O('x^50); concat([0], Vec(x*(1+x)/(1-x-2*x^2-x^3))) \\ G. C. Greubel, Jun 09 2017 CROSSREFS Cf. A000129, A140994, A140997. Sequence in context: A122584 A184936 A299106 * A141683 A142474 A078039 Adjacent sequences:  A141012 A141013 A141014 * A141016 A141017 A141018 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Jul 11 2008 EXTENSIONS Typo in definition corrected by Paolo P. Lava, Jul 31 2008 Dysfunctional Maple program removed by R. J. Mathar, Oct 28 2009 Comments clarified by Petros Hadjicostas, Jun 12 2019 STATUS approved

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Last modified October 13 19:35 EDT 2019. Contains 327981 sequences. (Running on oeis4.)