cp's OEIS Frontend

A210878 Triangle of coefficients of polynomials u(n,x) jointly generated with A210879; see the Formula section.

%I A210878 #5 Oct 02 2013 16:26:13
%S A210878 1,0,3,0,4,7,0,2,14,17,0,2,12,46,41,0,2,8,54,140,99,0,2,8,42,212,408,
%T A210878 239,0,2,8,34,200,758,1154,577,0,2,8,34,160,866,2544,3194,1393,0,2,8,
%U A210878 34,144,754,3448,8154,8696,3363,0,2,8,34,144,642,3400,12850
%N A210878 Triangle of coefficients of polynomials u(n,x) jointly generated with A210879; see the Formula section.
%C A210878 Leading coefficient of u(n,x):  A001333
%C A210878 Limiting row:  0,2,8,34,144,610,...(Fibonacci numbers)
%C A210878 For a discussion and guide to related arrays, see A208510.
%F A210878 u(n,x)=x*u(n-1,x)+2x*v(n-1,x),
%F A210878 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A210878 where u(1,x)=1, v(1,x)=1.
%e A210878 First six rows:
%e A210878 1
%e A210878 0...3
%e A210878 0...4...7
%e A210878 0...2...14...17
%e A210878 0...2...12...46...41
%e A210878 0...2...8....54...140...99
%e A210878 First three polynomials u(n,x): 1, 3x, 4x + 7x^2.
%t A210878 u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t A210878 u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x];
%t A210878 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210878 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210878 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210878 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210878 TableForm[cu]
%t A210878 Flatten[%]    (* A210878 *)
%t A210878 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210878 TableForm[cv]
%t A210878 Flatten[%]    (* A210879 *)
%Y A210878 Cf. A210879, A208510.
%K A210878 nonn,tabl
%O A210878 1,3
%A A210878 _Clark Kimberling_, Mar 30 2012