cp's OEIS Frontend

A210212 Triangle of coefficients of polynomials v(n,x) jointly generated with A210211; see the Formula section.

%I A210212 #4 Mar 30 2012 18:58:16
%S A210212 1,2,2,3,5,4,4,10,11,8,5,16,28,23,16,6,24,51,72,47,32,7,33,90,144,176,
%T A210212 95,64,8,44,138,294,377,416,191,128,9,56,208,492,878,938,960,383,256,
%U A210212 10,70,290,830,1577,2462,2251,2176,767,512,11,85,400,1250,2952
%N A210212 Triangle of coefficients of polynomials v(n,x) jointly generated with A210211; see the Formula section.
%C A210212 First and last terms of row n: n and 2^(n-1)
%C A210212 Alternating row sums are signed products of two Fibonacci numbers.
%C A210212 For a discussion and guide to related arrays, see A208510.
%F A210212 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210212 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A210212 where u(1,x)=1, v(1,x)=1.
%e A210212 First five rows:
%e A210212 1
%e A210212 2...2
%e A210212 3...5...4
%e A210212 4...10...11...8
%e A210212 5...16...28...23...16
%e A210212 First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 4x^2.
%t A210212 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210212 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210212 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210212 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210212 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210212 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210212 TableForm[cu]
%t A210212 Flatten[%]    (* A210211 *)
%t A210212 Table[Expand[v[n, x]], {n, 1, z}]
%t A210212 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210212 TableForm[cv]
%t A210212 Flatten[%]    (* A210212 *)
%Y A210212 Cf. A210211, A208510.
%K A210212 nonn,tabl
%O A210212 1,2
%A A210212 _Clark Kimberling_, Mar 19 2012