A209690 Triangle of coefficients of polynomials v(n,x) jointly generated with A209689; see the Formula section.

1, 2, 1, 1, 4, 1, 1, 3, 7, 1, 1, 2, 9, 11, 1, 1, 2, 6, 22, 16, 1, 1, 2, 5, 19, 46, 22, 1, 1, 2, 5, 14, 54, 86, 29, 1, 1, 2, 5, 13, 42, 135, 148, 37, 1, 1, 2, 5, 13, 35, 124, 302, 239, 46, 1, 1, 2, 5, 13, 34, 99, 341, 617, 367, 56, 1, 1, 2, 5, 13, 34, 90, 287, 860, 1171

Offset

1,2

Comments

Combinatorial limit of rows: odd-indexed Fibonacci numbers. For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..75.

Formula

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

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

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

Example

First five rows:
1
2...1
1...4...1
1...3...7...1
1...2...9...11...1
First three polynomials v(n,x): 1, 2 + x , 1 + 4x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := u[n - 1, x] + 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[%]   (* A209689 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209690 *)

Crossrefs

Cf. A209689, A208510.

Sequence in context: A306846 A327315 A141450 * A061462 A294334 A122578

Adjacent sequences: A209687 A209688 A209689 * A209691 A209692 A209693

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 12 2012

Status

approved