A210224 Triangle of coefficients of polynomials v(n,x) jointly generated with A210223; see the Formula section.

1, 1, 3, 1, 5, 5, 1, 5, 15, 7, 1, 5, 19, 35, 9, 1, 5, 19, 63, 69, 11, 1, 5, 19, 71, 177, 121, 13, 1, 5, 19, 71, 249, 429, 195, 15, 1, 5, 19, 71, 265, 781, 923, 295, 17, 1, 5, 19, 71, 265, 957, 2171, 1807, 425, 19, 1, 5, 19, 71, 265, 989, 3211, 5407, 3281, 589, 21

Offset

1,3

Comments

Limiting row: A001834

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

Links

Table of n, a(n) for n=1..66.

Formula

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

v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,

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

Example

First five rows:
1
1...3
1...5...5
1...5...15...7
1...5...19...35...9
First three polynomials v(n,x): 1, 1 + 3x , 1 + 5x + 5x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 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[%]     (* A210223 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210224 *)

Crossrefs

Cf. A210223, A208510.

Sequence in context: A351965 A228785 A135184 * A131304 A131302 A131305

Adjacent sequences: A210221 A210222 A210223 * A210225 A210226 A210227

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved