%I #6 Mar 30 2012 18:58:17
%S 1,1,3,1,4,8,1,4,14,21,1,4,15,46,55,1,4,15,55,145,144,1,4,15,56,196,
%T 444,377,1,4,15,56,208,678,1331,987,1,4,15,56,209,764,2282,3926,2584,
%U 1,4,15,56,209,779,2762,7499,11434,6765,1,4,15,56,209,780,2892
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210740; see the Formula section.
%C Rows end with even-indexed Fibonacci numbers
%C Limiting row: A001353
%C Row sums: A003562
%C Alternating row sums: A000975 (signed)
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e u(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%e v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%e where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...3
%e 1...4...8
%e 1...4...14...21
%e 1...4...15...46...55
%e First three polynomials u(n,x): 1, 1+ 3x, 1 + 4x + 8x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A210739 *)
%t Table[Expand[v[n, x]], {n, 1, z}]
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210740 *)
%Y Cf. A210740, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 24 2012