1,2

Row sums are: {1, 3, 6, 11, 21, 42, 85, 171, 342, 683, 1365}

c0=2; p(x, n) = (2 + c0 - x)*p(x, n - 1) + (-1 - c0 (2 - x))*p(x, n - 2) + c0*p(x, n - 3).

{1},

{4, -1},

{11, -6, 1},

{26, -22, 8, -1},

{57, -64, 37, -10, 1},

{120, -163, 130, -56, 12, -1},

{247, -382, 386, -232, 79, -14, 1},

{502, -848, 1024, -794, 378, -106, 16, -1},

{1013, -1816, 2510, -2380, 1471, -576, 137, -18, 1},

{2036, -3797, 5812, -6476, 4944, -2517, 834, -172, 20, -1},

{4083, -7814, 12911, -16384, 14893, -9402, 4048, -1160, 211, -22, 1}

Clear[p, c0, x, n, a] (* c0 = 0 : A136674 : Triangular sequence made from matrices of the type(Cartan G_n types) : M(3) = {{2, -1, 0}, {-1, 2, -1}, {0, -3, 2}} with polynomial recursion : p(x, n) = (2 - x)*p(x, n - 1) - p(x, n - 2). *) (* c0 = 1 : 1 : A109954 : Riordan array (1/(1 + x)^3, x/(1 + x)^2). *) c0 = 2; p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = 2 - x + c0; p[x_, n_] := p[x, n] = (2 + c0 - x)*p[x, n - 1] + (-1 - c0 (2 - x))*p[x, n - 2] + c0*p[x, n - 3]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]

Cf. A136674, A109954.

Sequence in context: A124324 A094503 A113897 this_sequence A109088 A060923 A097877

Adjacent sequences: A135549 A135550 A135551 this_sequence A135553 A135554 A135555

nonn,uned,tabl

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 08 2008