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 A100191 The (1,1)-entry in the 3 X 3 matrix M^n, where M = [1,2,1 / 2,2,0 / 1,0,0]. 2
 1, 6, 19, 73, 264, 973, 3565, 13086, 48007, 176149, 646296, 2371321, 8700553, 31923030, 117128107, 429752305, 1576795176, 5785386229, 21227039605, 77883687150, 285761407807, 1048481205661, 3846960466104, 14114802199681, 51788325586033, 190015462424934 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sequence generated from level 2 of the Pascal tetrahedron. REFERENCES Peter Hilton, Derek Holton and Jean Pederson, "Mathematical Vistas, From a Room With Many Windows"; Springer, 2000, p. 178, Fig. 14, "The Pascal Tetrahedron". LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,3,-2). FORMULA a(n) = 3*a(n-1) + 3*a(n-2) - 2*a(n-3) (derived from the minimal polynomial of the matrix M). G.f.: x*(1 + 3*x - 2*x^2) / (1 - 3*x - 3*x^2 + 2*x^3). - Colin Barker, Mar 02 2017 EXAMPLE a(4) = 73 because M^4 = [73,86,19 / 86,104,24 / 19,24,6]. Alternatively, a(4) = 3*a(3) + 3*a(2) - 2*a(1) = 57+18-2 = 73. MAPLE with(linalg): M[1]:=matrix(3, 3, [1, 2, 1, 2, 2, 0, 1, 0, 0]): for n from 2 to 27 do M[n]:=multiply(M[1], M[n-1]) od: seq(M[n][1, 1], n=1..27); a[1]:=1: a[2]:=6: a[3]:=19: for n from 4 to 27 do a[n]:=3*a[n-1]+3*a[n-2]-2*a[n-3] od: seq(a[n], n=1..27); PROG (PARI) Vec(x*(1 + 3*x - 2*x^2) / (1 - 3*x - 3*x^2 + 2*x^3) + O(x^30)) \\ Colin Barker, Mar 02 2017 CROSSREFS Cf. A100190. Sequence in context: A060579 A183326 A123950 * A191585 A220795 A026545 Adjacent sequences:  A100188 A100189 A100190 * A100192 A100193 A100194 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Nov 07 2004 EXTENSIONS Corrected by T. D. Noe, Nov 07 2006 Edited by N. J. A. Sloane, Dec 04 2006 STATUS approved

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Last modified December 15 15:10 EST 2019. Contains 329999 sequences. (Running on oeis4.)