A207634 Triangle of coefficients of polynomials v(n,x) jointly generated with A207633; see Formula section.

1, 2, 3, 3, 6, 6, 5, 13, 15, 12, 8, 26, 41, 36, 24, 13, 50, 95, 115, 84, 48, 21, 94, 210, 300, 302, 192, 96, 34, 173, 443, 740, 871, 760, 432, 192, 55, 314, 905, 1716, 2353, 2392, 1856, 960, 384, 89, 563, 1803, 3823, 5916, 6987, 6312, 4432, 2112, 768

Offset: 1

Author

Clark Kimberling, Feb 24 2012

Keywords

• nonn
• tabl

Comments

Column 1: Fibonacci numbers, A000045.

Examples

			First five rows:
1
2...3
3...6....6
5...13...15...12
8...26...41...36...24
		

Crossrefs

Cf. A207633.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]  (* A207633 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A207634 *)

Formula

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

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

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