A210752 Triangle of coefficients of polynomials v(n,x) jointly generated with A210751; see the Formula section.

1, 2, 3, 3, 8, 8, 4, 15, 27, 21, 5, 24, 61, 86, 55, 6, 35, 114, 227, 265, 144, 7, 48, 190, 484, 799, 798, 377, 8, 63, 293, 905, 1910, 2703, 2362, 987, 9, 80, 427, 1546, 3951, 7150, 8874, 6898, 2584, 10, 99, 596, 2471, 7391, 16188, 25711, 28455, 19929

Offset

1,2

Comments

Row n starts with n and ends with F(2n), where F=A000045 (Fibonacci numbers).

For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..54.

Formula

u(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,

v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

Example

First five rows:
1
2...3
3...8....8
4...15...27...21
5...24...61...86...55
First three polynomials v(n,x): 1, 2 + 3x, 3 + 8x +8x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A210751 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210752 *)

Crossrefs

Cf. A210751, A208510.

Sequence in context: A256679 A193997 A330048 * A210599 A211879 A308774

Adjacent sequences: A210749 A210750 A210751 * A210753 A210754 A210755

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 25 2012

Status

approved