A210227 Triangle of coefficients of polynomials u(n,x) jointly generated with A210228; see the Formula section.

1, 2, 1, 2, 6, 1, 2, 8, 16, 1, 2, 8, 32, 38, 1, 2, 8, 36, 112, 84, 1, 2, 8, 36, 156, 348, 178, 1, 2, 8, 36, 164, 620, 988, 368, 1, 2, 8, 36, 164, 732, 2244, 2624, 750, 1, 2, 8, 36, 164, 748, 3108, 7468, 6632, 1516, 1, 2, 8, 36, 164, 748, 3380, 12348, 23164

Offset

1,2

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)+1,

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
2...1
2...6...1
2...8...16...1
2...8...32...38...1
First three polynomials u(n,x): 1, 2 + x, 2 + 6x + 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] + 1;
v[n_, x_] := 2 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[%]     (* A210225 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210226 *)

Crossrefs

Cf. A210228, A208510.

Sequence in context: A361834 A166350 A357124 * A208757 A361830 A133643

Adjacent sequences: A210224 A210225 A210226 * A210228 A210229 A210230

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved