A209147 Triangle of coefficients of polynomials v(n,x) jointly generated with A209146; see the Formula section.

1, 2, 2, 3, 5, 4, 5, 11, 12, 8, 8, 23, 33, 28, 16, 13, 45, 80, 90, 64, 32, 21, 86, 180, 245, 232, 144, 64, 34, 160, 387, 615, 696, 576, 320, 128, 55, 293, 801, 1454, 1913, 1880, 1392, 704, 256, 89, 529, 1614, 3284, 4902, 5586, 4896, 3296, 1536, 512, 144

Offset

1,2

Comments

Each row begins with a Fibonacci numbers and ends with a power of 2. For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..56.

Formula

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

v(n,x)=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...2
3...5...4
5...11...12...8
8...23...33...28...16
First three polynomials v(n,x): 1, 2 + 2x, 3 + 5x + 4x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 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[%]    (* A209146 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209147 *)

Crossrefs

Cf. A209146, A208510.

Sequence in context: A334043 A301884 A302081 * A355059 A327267 A328666

Adjacent sequences: A209144 A209145 A209146 * A209148 A209149 A209150

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 06 2012

Status

approved