cp's OEIS Frontend

A210748 Triangle of coefficients of polynomials v(n,x) jointly generated with A210747; see the Formula section.

%I A210748 #5 Mar 30 2012 18:58:17
%S A210748 1,3,2,6,10,5,11,29,32,13,19,71,118,99,34,32,156,352,437,299,89,53,
%T A210748 322,919,1521,1526,887,233,87,636,2205,4559,6036,5117,2595,610,142,
%U A210748 1218,4979,12373,20320,22591,16653,7508,1597,231,2279,10751,31233
%N A210748 Triangle of coefficients of polynomials v(n,x) jointly generated with A210747; see the Formula section.
%C A210748 Row n starts with -2+F(n+3) and ends with F(2n-1), where F=A000045 (Fibonacci numbers).
%C A210748 Row sums: A002450
%C A210748 Alternating row sums:  1,1,1,1,1,1,1,1,1,...(A000012)
%C A210748 For a discussion and guide to related arrays, see A208510.
%F A210748 u(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210748 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210748 where u(1,x)=1, v(1,x)=1.
%e A210748 First five rows:
%e A210748 1
%e A210748 3....2
%e A210748 6....10...5
%e A210748 11...29...32....13
%e A210748 19...71...118...99...34
%e A210748 First three polynomials v(n,x): 1, 3 + 2x, 6 + 10x +5x^2
%t A210748 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210748 u[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210748 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210748 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210748 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210748 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210748 TableForm[cu]
%t A210748 Flatten[%]   (* A210747 *)
%t A210748 Table[Expand[v[n, x]], {n, 1, z}]
%t A210748 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210748 TableForm[cv]
%t A210748 Flatten[%]   (* A210748 *)
%t A210748 Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A002450 *)
%t A210748 Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A002450 *)
%t A210748 Table[u[n, x] /. x -> -1, {n, 1, z}] (* A077925 *)
%t A210748 Table[v[n, x] /. x -> -1, {n, 1, z}] (* A000012 *)
%Y A210748 Cf. A210747, A208510.
%K A210748 nonn,tabl
%O A210748 1,2
%A A210748 _Clark Kimberling_, Mar 25 2012