A210599 Triangle of coefficients of polynomials v(n,x) jointly generated with A210221; see the Formula section.

1, 2, 3, 3, 8, 8, 4, 16, 28, 21, 5, 26, 69, 92, 55, 6, 39, 134, 268, 290, 144, 7, 54, 233, 606, 974, 888, 377, 8, 72, 368, 1196, 2510, 3378, 2662, 987, 9, 92, 550, 2122, 5541, 9760, 11313, 7852, 2584, 10, 115, 780, 3510, 10900, 23825, 36188, 36872

Offset

1,2

Comments

Row n starts with n and ends with an even-indexed Fibonacci number. For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..53.

Formula

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

v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,

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

Example

First five rows:
1
2...3
3...8....8
4...16...28...21
5...26...69...92...55
First three polynomials v(n,x): 1, 2 + 3x, 3 + 8x + 8x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%]    (* A210598 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210599 *)

Crossrefs

Cf. A210598, A208510.

Sequence in context: A193997 A330048 A210752 * A211879 A308774 A308859

Adjacent sequences: A210596 A210597 A210598 * A210600 A210601 A210602

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 24 2012

Status

approved