cp's OEIS Frontend

A210802 Triangle of coefficients of polynomials v(n,x) jointly generated with A210801; see the Formula section.

%I A210802 #5 Mar 30 2012 18:58:17
%S A210802 1,2,2,5,5,3,8,16,11,5,17,34,40,22,8,26,82,107,93,43,13,53,163,287,
%T A210802 287,201,81,21,80,352,674,862,709,419,150,34,161,676,1592,2272,2326,
%U A210802 1641,845,273,55,242,1378,3482,5878,6797,5863,3638,1666,491,89,485
%N A210802 Triangle of coefficients of polynomials v(n,x) jointly generated with A210801; see the Formula section.
%C A210802 Row n ends with F(n+1), where F=A000045 (Fibonacci numbers).
%C A210802 Row sums: A003462
%C A210802 Alternating row sums: A077898
%C A210802 For a discussion and guide to related arrays, see A208510.
%F A210802 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210802 v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x)+1,
%F A210802 where u(1,x)=1, v(1,x)=1.
%e A210802 First five rows:
%e A210802 1
%e A210802 2....2
%e A210802 5....5....3
%e A210802 8....16...11...5
%e A210802 17...34...40...22...8
%e A210802 First three polynomials v(n,x): 1, 2 + 2x, 5 + 5x + 3x^2
%t A210802 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210802 u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
%t A210802 d[x_] := h + x; e[x_] := p + x;
%t A210802 v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
%t A210802 j = 1; c = 1; h = 2; p = -1; f = 1;
%t A210802 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210802 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210802 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210802 TableForm[cu]
%t A210802 Flatten[%]   (* A210801 *)
%t A210802 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210802 TableForm[cv]
%t A210802 Flatten[%]   (* A210802 *)
%t A210802 Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A003462 *)
%t A210802 Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A003462 *)
%t A210802 Table[u[n, x] /. x -> -1, {n, 1, z}] (* A000027 *)
%t A210802 Table[v[n, x] /. x -> -1, {n, 1, z}] (* A077898 *)
%Y A210802 Cf. A210801, A208510.
%K A210802 nonn,tabl
%O A210802 1,2
%A A210802 _Clark Kimberling_, Mar 27 2012