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A210549 Triangle of coefficients of polynomials u(n,x) jointly generated with A210550; see the Formula section.

%I A210549 #6 Mar 30 2012 18:58:16
%S A210549 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 A210549 64,1,3,10,34,115,311,385,128,1,3,10,34,116,381,886,897,256,1,3,10,34,
%U A210549 116,395,1224,2421,2049,512,1,3,10,34,116,396,1334,3796,6388
%N A210549 Triangle of coefficients of polynomials u(n,x) jointly generated with A210550; see the Formula section.
%C A210549 Each row begins with 1 and ends with 2^(n-1).
%C A210549 Row sums: 1,3,8,21,..., the even-indexed Fibonacci numbers
%C A210549 For a discussion and guide to related arrays, see A208510.
%F A210549 u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A210549 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A210549 where u(1,x)=1, v(1,x)=1.
%e A210549 First five rows:
%e A210549 1
%e A210549 1...2
%e A210549 1...3...4
%e A210549 1...3...9....8
%e A210549 1...3...10...25...16
%e A210549 First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 4x^2.
%t A210549 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210549 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210549 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210549 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210549 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210549 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210549 TableForm[cu]
%t A210549 Flatten[%]      (* A210235 *)
%t A210549 Table[Expand[v[n, x]], {n, 1, z}]
%t A210549 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210549 TableForm[cv]
%t A210549 Flatten[%]      (* A210236 *)
%Y A210549 Cf. A210550, A208510.
%K A210549 nonn,tabl
%O A210549 1,3
%A A210549 _Clark Kimberling_, Mar 22 2012