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A210211 Triangle of coefficients of polynomials u(n,x) jointly generated with A210212; see the Formula section.

%I A210211 #7 Jul 12 2012 00:40:00
%S A210211 1,2,1,3,4,1,4,8,8,1,5,14,19,16,1,6,21,42,42,32,1,7,30,72,114,89,64,1,
%T A210211 8,40,120,216,290,184,128,1,9,52,178,414,593,706,375,256,1,10,65,260,
%U A210211 670,1292,1531,1666,758,512,1,11,80,355,1090,2247,3754,3782
%N A210211 Triangle of coefficients of polynomials u(n,x) jointly generated with A210212; see the Formula section.
%C A210211 Row n starts with n and ends with 2^n followed by 1.
%C A210211 n-th row sum: F(2k), where F=A000045 (Fibonacci numbers)
%C A210211 Alternating row sums are signed products of two Fibonacci numbers.
%C A210211 For a discussion and guide to related arrays, see A208510.
%F A210211 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210211 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A210211 where u(1,x)=1, v(1,x)=1.
%e A210211 First five rows:
%e A210211 1
%e A210211 2...1
%e A210211 3...4....1
%e A210211 4...8....8....1
%e A210211 5...14...19...16...1
%e A210211 First three polynomials u(n,x): 1, 2 + x, 3 + 4x + x^2.
%t A210211 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210211 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210211 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210211 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210211 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210211 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210211 TableForm[cu]
%t A210211 Flatten[%]    (* A210211 *)
%t A210211 Table[Expand[v[n, x]], {n, 1, z}]
%t A210211 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210211 TableForm[cv]
%t A210211 Flatten[%]    (* A210212 *)
%Y A210211 Cf. A210204, A208510.
%K A210211 nonn,tabl
%O A210211 1,2
%A A210211 _Clark Kimberling_, Mar 19 2012