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

1, 1, 4, 1, 6, 10, 1, 6, 24, 22, 1, 6, 28, 80, 46, 1, 6, 28, 120, 236, 94, 1, 6, 28, 128, 464, 640, 190, 1, 6, 28, 128, 568, 1624, 1636, 382, 1, 6, 28, 128, 584, 2376, 5224, 4008, 766, 1, 6, 28, 128, 584, 2632, 9240, 15696, 9516, 1534, 1, 6, 28, 128, 584

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..60.

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
1...4
1...6...10
1...6...24...22
1...6...28...80...46
First three polynomials v(n,x): 1, 1 + 4x , 1 + 6x + 19x^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] + 2 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[%]     (* A210227 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210228 *)

Crossrefs

Cf. A210227, A208510.

Sequence in context: A154905 A124739 A122662 * A209161 A338171 A333824

Adjacent sequences: A210225 A210226 A210227 * A210229 A210230 A210231

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved