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 A210793 Triangle of coefficients of polynomials u(n,x) jointly generated with A210794; see the Formula section. 3
 1, 2, 1, 3, 4, 2, 6, 10, 8, 3, 9, 24, 27, 16, 5, 18, 51, 74, 62, 30, 8, 27, 108, 189, 200, 136, 56, 13, 54, 216, 450, 574, 488, 282, 102, 21, 81, 432, 1026, 1536, 1571, 1128, 569, 184, 34, 162, 837, 2268, 3864, 4598, 3967, 2486, 1118, 328, 55, 243, 1620 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n starts with A038754(n) and ends with F(n), where F=A000045 (Fibonacci numbers). Row sums: A000244 (powers of 3). Alternating row sums: A000012 (1,1,1,1,1,1,1,1,1,1,1,...). For a discussion and guide to related arrays, see A208510. Subtriangle of the triangle given by (1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 29 2012 LINKS FORMULA u(n,x) = u(n-1,x) + (x+1)*v(n-1,x), v(n,x) = (x+2)*u(n-1,x) + (x-1)*v(n-1,x), where u(1,x)=1, v(1,x)=1. From Philippe Deléham, Mar 29 2012: (Start) As DELTA(triangle T(n,k) with 0 <= k <= n: G.f.: (1 + x - y*x^2 - 2*y*x^2 - y^2*x^2)/(1 - y*x - 3*x^2 - 2*y*x^2 - y^2*x^2). T(n,k) = T(n-1,k-1) + 3*T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-2), T(0,0) = T(1,0) = T(2,1) = 1, T(2,0) = 2, T(1,1) = T(2,2) = 0 and T(n,k) = 0 if k < 0 or if k <= n. EXAMPLE First five rows:   1;   2,  1;   3,  4,  2;   6, 10,  8,  3;   9, 24, 27, 16,  5; First three polynomials u(n,x):   1   2 + x   3 + 4x + 2x^2. From Philippe Deléham, Mar 29 2012: (Start) (1, 1, -1, -1, 0, 0, 0, ...) DELTA (0, 1, 1, -1, 0, 0, 0, ...) begins:    1;    1,  0;    2,  1,  0;    3,  4,  2,  0;    6, 10,  8,  3,  0;    9, 24, 27, 16,  5,  0;   18, 51, 74, 62, 30,  8,  0; (End) MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c; d[x_] := h + x; e[x_] := p + x; v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f; j = 1; c = 0; h = 2; p = -1; f = 0; Table[Expand[u[n, x]], {n, 1, z/2}] Table[Expand[v[n, x]], {n, 1, z/2}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%]   (* A210793 *) cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A210794 *) Table[u[n, x] /. x -> 1, {n, 1, z}]   (* A000244 *) Table[v[n, x] /. x -> 1, {n, 1, z}]   (* A000244 *) Table[u[n, x] /. x -> -1, {n, 1, z}]  (* A000012 *) Table[v[n, x] /. x -> -1, {n, 1, z}]  (* A077925 *) CROSSREFS Cf. A210794, A208510. Sequence in context: A209137 A269752 A122164 * A281715 A076632 A105646 Adjacent sequences:  A210790 A210791 A210792 * A210794 A210795 A210796 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 26 2012 STATUS approved

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Last modified January 25 08:01 EST 2021. Contains 340416 sequences. (Running on oeis4.)