A210218 Triangle of coefficients of polynomials v(n,x) jointly generated with A210217; see the Formula section.

1, 1, 3, 1, 4, 7, 1, 4, 13, 15, 1, 4, 14, 38, 31, 1, 4, 14, 47, 103, 63, 1, 4, 14, 48, 151, 264, 127, 1, 4, 14, 48, 163, 462, 649, 255, 1, 4, 14, 48, 164, 544, 1348, 1546, 511, 1, 4, 14, 48, 164, 559, 1768, 3769, 3595, 1023, 1, 4, 14, 48, 164, 560, 1893, 5564

Offset

1,3

Comments

Limiting row: A007070

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)=x*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...3
1...4...7
1...4...13...15
1...4...14...38...31
First three polynomials v(n,x): 1, 1 + 3x , 1 + 4x + 7x^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*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[%]    (* A210217 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210218 *)

Crossrefs

Cf. A210217, A208510.

Sequence in context: A028861 A081521 A213224 * A086273 A054143 A104746

Adjacent sequences: A210215 A210216 A210217 * A210219 A210220 A210221

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 19 2012

Status

approved