A209566 Triangle of coefficients of polynomials v(n,x) jointly generated with A209565; see the Formula section.

1, 1, 3, 1, 3, 7, 1, 3, 10, 15, 1, 3, 10, 31, 31, 1, 3, 10, 34, 88, 63, 1, 3, 10, 34, 113, 233, 127, 1, 3, 10, 34, 116, 359, 586, 255, 1, 3, 10, 34, 116, 393, 1084, 1419, 511, 1, 3, 10, 34, 116, 396, 1306, 3120, 3340, 1023, 1, 3, 10, 34, 116, 396, 1349, 4216

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..63.

Formula

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

v(n,x)=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
1...1
1...4...1
1...4...11...1
1...4...14...26...1
First three polynomials v(n,x): 1, 1 + x , 1 + 4x + x^2 .

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := 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[%]   (* A209565 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209566 *)

Crossrefs

Cf. A209565, A208510.

Sequence in context: A094250 A208517 A336203 * A208916 A209766 A356207

Adjacent sequences: A209563 A209564 A209565 * A209567 A209568 A209569

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved