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A210744 Triangle of coefficients of polynomials v(n,x) jointly generated with A210743; see the Formula section.

%I A210744 #5 Mar 30 2012 18:58:17
%S A210744 1,3,1,6,6,3,11,18,18,7,19,45,63,49,17,32,100,182,200,133,41,53,208,
%T A210744 464,658,613,356,99,87,413,1094,1886,2244,1823,944,239,142,794,2437,
%U A210744 4940,7093,7325,5302,2483,577,231,1490,5206,12113,20311,25220
%N A210744 Triangle of coefficients of polynomials v(n,x) jointly generated with A210743; see the Formula section.
%C A210744 Row n starts with -2+F(n+3), where F=A000045 (Fibonacci numbers) and ends with A001333(n-1).
%C A210744 Alternating  row sums: 1,2,3,4,5,6,7,8,...
%C A210744 For a discussion and guide to related arrays, see A208510.
%F A210744 u(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210744 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210744 where u(1,x)=1, v(1,x)=1.
%e A210744 First five rows:
%e A210744 1
%e A210744 3....1
%e A210744 6....6....3
%e A210744 11...18...18...7
%e A210744 19...45...63...49...17
%e A210744 First three polynomials v(n,x): 1, 3 + x, 6 + 6x +3x^2
%t A210744 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210744 u[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210744 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210744 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210744 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210744 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210744 TableForm[cu]
%t A210744 Flatten[%]      (* A210743 *)
%t A210744 Table[Expand[v[n, x]], {n, 1, z}]
%t A210744 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210744 TableForm[cv]
%t A210744 Flatten[%]      (* A210744 *)
%Y A210744 Cf. A210743, A208510.
%K A210744 nonn,tabl
%O A210744 1,2
%A A210744 _Clark Kimberling_, Mar 24 2012