A209691 Triangle of coefficients of polynomials u(n,x) jointly generated with A209692; see the Formula section.

1, 0, 2, 0, 2, 4, 0, 1, 8, 8, 0, 1, 5, 24, 16, 0, 1, 4, 21, 64, 32, 0, 1, 4, 15, 77, 160, 64, 0, 1, 4, 14, 58, 253, 384, 128, 0, 1, 4, 14, 49, 221, 765, 896, 256, 0, 1, 4, 14, 48, 177, 800, 2173, 2048, 512, 0, 1, 4, 14, 48, 165, 654, 2723, 5885, 4608, 1024, 0, 1, 4

Offset

1,3

Comments

Combinatorial limit of rows: A007070.

For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..69.

Formula

u(n,x)=x*u(n-1,x)+x*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
0...2
0...2...4
0...1...8...8
0...1...5...24...16
First three polynomials v(n,x): 1, 2x, 2x + 4x^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] + 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[%]   (* A209691 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209692 *)

Crossrefs

Cf. A209692, A208510.

Sequence in context: A136716 A117946 A061930 * A221683 A332760 A199335

Adjacent sequences: A209688 A209689 A209690 * A209692 A209693 A209694

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 12 2012

Status

approved