A209576 Triangle of coefficients of polynomials v(n,x) jointly generated with A209575; see the Formula section.

1, 1, 4, 1, 4, 10, 1, 4, 18, 22, 1, 4, 18, 66, 46, 1, 4, 18, 82, 206, 94, 1, 4, 18, 82, 342, 578, 190, 1, 4, 18, 82, 374, 1274, 1510, 382, 1, 4, 18, 82, 374, 1642, 4294, 3754, 766, 1, 4, 18, 82, 374, 1706, 6726, 13354, 9006, 1534, 1, 4, 18, 82, 374, 1706

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..61.

Formula

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

v(n,x)=2x*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...4
1...4...10
1...4...18...22
1...4...18...66...46
First three polynomials v(n,x): 1, 1+4x, 1+4x+10x^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_] := 2 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[%]   (* A209575 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209576 *)

Crossrefs

Cf. A209575, A208510.

Sequence in context: A201286 A347221 A208527 * A055886 A132478 A208918

Adjacent sequences: A209573 A209574 A209575 * A209577 A209578 A209579

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 11 2012

Status

approved