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

Author

Clark Kimberling, Mar 06 2012

Keywords

• nonn
• tabl

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.

Examples

			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.
		

Crossrefs

Cf. A209146, A208510.

Programs

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 *)

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.