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

1,2

Comments

Column 1: Fibonacci numbers, A000045.

Links

Table of n, a(n) for n=1..55.

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.

Example

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

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 *)

Crossrefs

Cf. A207633.

Sequence in context: A321745 A212629 A127779 * A222862 A101437 A039856

Adjacent sequences: A207631 A207632 A207633 * A207635 A207636 A207637

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 24 2012

Status

approved