A210187 Triangle of coefficients of polynomials u(n,x) jointly generated with A210188; see the Formula section.

1, 3, 6, 2, 10, 9, 2, 15, 25, 13, 2, 21, 55, 49, 17, 2, 28, 105, 140, 81, 21, 2, 36, 182, 336, 285, 121, 25, 2, 45, 294, 714, 825, 506, 169, 29, 2, 55, 450, 1386, 2079, 1716, 819, 225, 33, 2, 66, 660, 2508, 4719, 5005, 3185, 1240, 289, 37, 2, 78, 935, 4290

Offset

1,2

Comments

Row sums: even-indexed Fibonacci numbers: 1,3,8,21,55,...

Column 1: triangular numbers: A000217

Alternating row sums: periodic with period (1,3,4,3,1,0)

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

Links

Table of n, a(n) for n=1..59.

Formula

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

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

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

Example

First five rows:
1
3
6....2
10...9....2
15...25...13...2
First three polynomials u(n,x): 1, 3, 6 + 2x.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 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[%]    (* A210187 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210188 *)

Crossrefs

Cf. A210188, A208510.

Sequence in context: A360255 A353989 A354087 * A364365 A210189 A257506

Adjacent sequences: A210184 A210185 A210186 * A210188 A210189 A210190

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 18 2012

Status

approved