|
%I #5 Mar 30 2012 18:58:17
%S 1,2,3,3,8,8,4,16,28,21,5,26,69,92,55,6,39,134,268,290,144,7,54,233,
%T 606,974,888,377,8,72,368,1196,2510,3378,2662,987,9,92,550,2122,5541,
%U 9760,11313,7852,2584,10,115,780,3510,10900,23825,36188,36872
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210221; see the Formula section.
%C Row n starts with n and ends with an even-indexed Fibonacci number. For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...3
%e 3...8....8
%e 4...16...28...21
%e 5...26...69...92...55
%e First three polynomials v(n,x): 1, 2 + 3x, 3 + 8x + 8x^2
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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[%] (* A210598 *)
%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[%] (* A210599 *)
%Y Cf. A210598, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 24 2012
|
