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%I #6 Mar 30 2012 18:58:16
%S 1,1,2,1,3,4,1,3,9,8,1,3,10,25,16,1,3,10,33,65,32,1,3,10,34,104,161,
%T 64,1,3,10,34,115,311,385,128,1,3,10,34,116,381,886,897,256,1,3,10,34,
%U 116,395,1224,2421,2049,512,1,3,10,34,116,396,1334,3796,6388
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210550; see the Formula section.
%C Each row begins with 1 and ends with 2^(n-1).
%C Row sums: 1,3,8,21,..., the even-indexed Fibonacci numbers
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...2
%e 1...3...4
%e 1...3...9....8
%e 1...3...10...25...16
%e First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 4x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*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[%] (* A210235 *)
%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[%] (* A210236 *)
%Y Cf. A210550, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 22 2012
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