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A210601 Triangle of coefficients of polynomials v(n,x) jointly generated with A210600; see the Formula section.

%I A210601 #5 Mar 30 2012 18:58:17
%S A210601 1,3,2,6,9,4,11,26,24,8,19,63,89,60,16,32,138,265,270,144,32,53,284,
%T A210601 693,949,760,336,64,87,560,1664,2870,3072,2032,768,128,142,1071,3761,
%U A210601 7840,10521,9272,5232,1728,256,231,2002,8127,19896,32143,35418
%N A210601 Triangle of coefficients of polynomials v(n,x) jointly generated with A210600; see the Formula section.
%C A210601 Row n starts with n and ends with an even-indexed Fibonacci number.  For a discussion and guide to related arrays, see A208510.
%F A210601 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A210601 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210601 where u(1,x)=1, v(1,x)=1.
%e A210601 First five rows:
%e A210601 1
%e A210601 3....2
%e A210601 6....9....4
%e A210601 11...26...24...8
%e A210601 19...63...89...60...16
%e A210601 First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x + 4x^2
%t A210601 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210601 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210601 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210601 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210601 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210601 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210601 TableForm[cu]
%t A210601 Flatten[%]    (* A210600 *)
%t A210601 Table[Expand[v[n, x]], {n, 1, z}]
%t A210601 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210601 TableForm[cv]
%t A210601 Flatten[%]    (* A210601 *)
%Y A210601 Cf. A210600, A208510.
%K A210601 nonn,tabl
%O A210601 1,2
%A A210601 _Clark Kimberling_, Mar 24 2012