A210231 Triangle of coefficients of polynomials u(n,x) jointly generated with A210232; see the Formula section.

1, 2, 1, 3, 4, 1, 4, 8, 7, 1, 5, 14, 18, 11, 1, 6, 21, 39, 36, 16, 1, 7, 30, 69, 93, 66, 22, 1, 8, 40, 114, 192, 199, 113, 29, 1, 9, 52, 172, 360, 474, 393, 183, 37, 1, 10, 65, 250, 610, 997, 1068, 729, 283, 46, 1, 11, 80, 345, 980, 1882, 2501, 2238, 1285, 421

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..64.

Formula

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

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

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

Example

First five rows:
1
2...1
3...4....1
4...8....7....1
5...14...18...11...1
First three polynomials u(n,x): 1, 2 + x, 3 + 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] + 1;
v[n_, x_] := (x + 1)*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[%]     (* A210231 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210232 *)

Crossrefs

Cf. A210232, A208510.

Sequence in context: A072506 A188236 A181851 * A180378 A208341 A201634

Adjacent sequences: A210228 A210229 A210230 * A210232 A210233 A210234

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved