A210738 Triangle of coefficients of polynomials v(n,x) jointly generated with A210603; see the Formula section.

1, 3, 2, 6, 9, 4, 11, 25, 23, 8, 19, 60, 81, 55, 16, 32, 130, 237, 233, 127, 32, 53, 266, 610, 798, 625, 287, 64, 87, 522, 1451, 2364, 2439, 1601, 639, 128, 142, 995, 3255, 6373, 8138, 6984, 3969, 1407, 256, 231, 1855, 6995, 16007, 24430, 25832

Offset

1,2

Comments

Row n starts with F(n+3)-2, where F=A000045 (Fibonacci

numbers), and ends with 2^(n-1). For a discussion and

guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..51.

Formula

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

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

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

Example

First five rows:
1
3....2
6....9....4
11...25...23...8
19...60...81...55...16
First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x + 4x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*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[%]    (* A210603 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210738 *)

Crossrefs

Cf. A210603, A208510.

Sequence in context: A318049 A352877 A210754 * A210601 A197493 A300070

Adjacent sequences: A210735 A210736 A210737 * A210739 A210740 A210741

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 24 2012

Status

approved