A210202 Triangle of coefficients of polynomials v(n,x) jointly generated with A210201; see the Formula section.

1, 2, 3, 4, 7, 6, 7, 17, 17, 12, 12, 35, 50, 40, 24, 20, 70, 120, 135, 92, 48, 33, 134, 275, 365, 346, 208, 96, 54, 251, 593, 930, 1033, 856, 464, 192, 88, 461, 1236, 2206, 2874, 2784, 2064, 1024, 384, 143, 835, 2500, 5015, 7389, 8355, 7240, 4880

Offset

1,2

Comments

Column 1: F(n+2)-1, where F=A000045 (Fibonacci numbers)

Row sums: A048473

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

Links

Table of n, a(n) for n=1..53.

Formula

u(n,x)=u(n-1,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
4....7....6
7....17...17...12
12...35...50...40...24
First three polynomials v(n,x): 1, 2 + 3x , 4 + 7x + 6x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, 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[%]   (* A210201 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210202 *)

Crossrefs

Cf. A210201, A208510.

Sequence in context: A120225 A247798 A130685 * A358201 A358176 A359682

Adjacent sequences: A210199 A210200 A210201 * A210203 A210204 A210205

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 18 2012

Status

approved