|
%I #5 Oct 02 2013 16:26:13
%S 1,2,2,1,5,5,1,5,16,12,1,3,21,47,29,1,3,17,79,134,70,1,3,13,79,273,
%T 373,169,1,3,13,63,333,893,1020,408,1,3,13,55,297,1291,2805,2751,985,
%U 1,3,13,55,249,1323,4701,8543,7338,2378,1,3,13,55,233,1147,5525
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210878; see the Formula section.
%C Leading coefficient of v(n,x): A000129
%C Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...
%C Limiting row: 1,3,13,55,233,987...( Fibonacci numbers)
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+2x*v(n-1,x),
%F v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First six rows:
%e 1
%e 2...2
%e 1...5...5
%e 1...5...16...12
%e 1...3...21...47....29
%e 1...3...17...79...134...70
%e First three polynomials v(n,x): 1, 2 + 2x, 1 + 5x + 5x^2
%t u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x];
%t v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A210878 *)
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210879 *)
%Y Cf. A210878, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 30 2012
|
