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

Author

Clark Kimberling, Mar 24 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			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
		

Crossrefs

Cf. A210600, A208510.

Programs

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 *)

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.