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

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
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
		

Crossrefs

Cf. A210598, 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] + 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 *)

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.