cp's OEIS Frontend

A210229 Triangle of coefficients of polynomials u(n,x) jointly generated with A210230; see the Formula section.

%I A210229 #4 Mar 30 2012 18:58:16
%S A210229 1,2,1,4,3,1,7,8,4,1,12,18,13,5,1,20,38,35,19,6,1,33,76,86,59,26,7,1,
%T A210229 54,147,197,164,91,34,8,1,88,277,430,420,281,132,43,9,1,143,512,904,
%U A210229 1014,792,447,183,53,10,1,232,932,1846,2338,2087,1371,673,245,64
%N A210229 Triangle of coefficients of polynomials u(n,x) jointly generated with A210230; see the Formula section.
%C A210229 Column 1:  -1+F(n+1), where F=A000045 (Fibonacci numbers)
%C A210229 Alternating row sums: 1,1,2,2,3,3,4,4,5,5,...
%C A210229 For a discussion and guide to related arrays, see A208510.
%F A210229 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210229 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210229 where u(1,x)=1, v(1,x)=1.
%e A210229 First five rows:
%e A210229 1
%e A210229 2....1
%e A210229 4....3....1
%e A210229 7....8....4....1
%e A210229 12...18...13...5...1
%e A210229 First three polynomials u(n,x): 1, 2 + x, 4 + 3x + x^2.
%t A210229 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210229 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210229 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210229 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210229 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210229 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210229 TableForm[cu]
%t A210229 Flatten[%]     (* A210229 *)
%t A210229 Table[Expand[v[n, x]], {n, 1, z}]
%t A210229 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210229 TableForm[cv]
%t A210229 Flatten[%]     (* A210230 *)
%Y A210229 Cf. A210230, A208510.
%K A210229 nonn,tabl
%O A210229 1,2
%A A210229 _Clark Kimberling_, Mar 20 2012