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

1, 2, 1, 2, 5, 1, 2, 7, 10, 1, 2, 7, 22, 17, 1, 2, 7, 26, 57, 26, 1, 2, 7, 26, 89, 126, 37, 1, 2, 7, 26, 97, 266, 247, 50, 1, 2, 7, 26, 97, 346, 695, 442, 65, 1, 2, 7, 26, 97, 362, 1127, 1618, 737, 82, 1, 2, 7, 26, 97, 362, 1319, 3298, 3425, 1162, 101, 1, 2, 7, 26

Offset

1,2

Comments

Limiting row: A001075

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

Links

Table of n, a(n) for n=1..69.

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
2...1
2...5...1
2...7...10...1
2...7...22...17...1
First three polynomials u(n,x): 1, 2 + x, 2 + 5x + 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*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. A210224, A208510.

Sequence in context: A210217 A334165 A370887 * A361600 A242598 A225568

Adjacent sequences: A210220 A210221 A210222 * A210224 A210225 A210226

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved