%I #4 Mar 30 2012 18:58:16
%S 1,2,1,4,3,1,7,8,4,1,12,18,13,5,1,20,38,35,19,6,1,33,76,86,59,26,7,1,
%T 54,147,197,164,91,34,8,1,88,277,430,420,281,132,43,9,1,143,512,904,
%U 1014,792,447,183,53,10,1,232,932,1846,2338,2087,1371,673,245,64
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210230; see the Formula section.
%C Column 1: -1+F(n+1), where F=A000045 (Fibonacci numbers)
%C Alternating row sums: 1,1,2,2,3,3,4,4,5,5,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2....1
%e 4....3....1
%e 7....8....4....1
%e 12...18...13...5...1
%e First three polynomials u(n,x): 1, 2 + x, 4 + 3x + x^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] + 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[%] (* A210229 *)
%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[%] (* A210230 *)
%Y Cf. A210230, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 20 2012
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