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A210597 Triangle of coefficients of polynomials u(n,x) jointly generated with A210602; see the Formula section.

%I A210597 #5 Mar 30 2012 18:58:17
%S A210597 1,2,2,4,5,4,7,13,12,8,12,28,37,28,16,20,58,92,98,64,32,33,114,217,
%T A210597 273,248,144,64,54,218,479,713,760,608,320,128,88,407,1018,1727,2161,
%U A210597 2024,1456,704,256,143,747,2093,3997,5662,6194,5216,3424,1536,512
%N A210597 Triangle of coefficients of polynomials u(n,x) jointly generated with A210602; see the Formula section.
%C A210597 Row n starts with F(n+2)-1, where F=A000045 (Fibonacci
%C A210597 numbers), and ends with 2^(n-1).  For a discussion and
%C A210597 guide to related arrays, see A208510.
%F A210597 u(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A210597 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210597 where u(1,x)=1, v(1,x)=1.
%e A210597 First five rows:
%e A210597 1
%e A210597 2....2
%e A210597 4....5....4
%e A210597 7....13...12...8
%e A210597 12...28...37...28...16
%e A210597 First three polynomials u(n,x): 1, 2+ 2x, 4 + 5x + 4x^2.
%t A210597 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210597 u[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210597 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210597 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210597 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210597 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210597 TableForm[cu]
%t A210597 Flatten[%]    (* A210597 *)
%t A210597 Table[Expand[v[n, x]], {n, 1, z}]
%t A210597 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210597 TableForm[cv]
%t A210597 Flatten[%]    (* A210602 *)
%Y A210597 Cf. A210602, A208510.
%K A210597 nonn,tabl
%O A210597 1,2
%A A210597 _Clark Kimberling_, Mar 24 2012