A209559 Triangle of coefficients of polynomials u(n,x) jointly generated with A209560; see the Formula section.

1, 1, 1, 3, 2, 1, 5, 8, 3, 1, 9, 17, 15, 4, 1, 15, 38, 39, 24, 5, 1, 25, 76, 104, 74, 35, 6, 1, 41, 149, 242, 229, 125, 48, 7, 1, 67, 282, 543, 607, 440, 195, 63, 8, 1, 109, 524, 1159, 1531, 1308, 769, 287, 80, 9, 1, 177, 957, 2401, 3631, 3660, 2533, 1253, 404

Offset

1,4

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

where u(1,x)=1, v(1,x)=1.

Example

First five rows:
1
1...1
3...2....1
5...8....3....1
9...17...15...4...1
First three polynomials v(n,x): 1, 1 + x, 3 + 2x + 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_] := u[n - 1, x] + (x + 1)*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[%]   (* A209559 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209560 *)

Crossrefs

Cf. A209560, A208510.

Sequence in context: A208511 A129675 A232206 * A081277 A079628 A140287

Adjacent sequences: A209556 A209557 A209558 * A209560 A209561 A209562

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved