A210601 Triangle of coefficients of polynomials v(n,x) jointly generated with A210600; see the Formula section.

1, 3, 2, 6, 9, 4, 11, 26, 24, 8, 19, 63, 89, 60, 16, 32, 138, 265, 270, 144, 32, 53, 284, 693, 949, 760, 336, 64, 87, 560, 1664, 2870, 3072, 2032, 768, 128, 142, 1071, 3761, 7840, 10521, 9272, 5232, 1728, 256, 231, 2002, 8127, 19896, 32143, 35418

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..51.

Formula

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

v(n,x)=(x+1)*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....2
6....9....4
11...26...24...8
19...63...89...60...16
First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x + 4x^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] + (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[%]    (* A210600 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210601 *)

Crossrefs

Cf. A210600, A208510.

Sequence in context: A352877 A210754 A210738 * A197493 A300070 A171632

Adjacent sequences: A210598 A210599 A210600 * A210602 A210603 A210604

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 24 2012

Status

approved