A209760 Triangle of coefficients of polynomials v(n,x) jointly generated with A209759; see the Formula section.

1, 1, 3, 1, 3, 8, 1, 3, 11, 21, 1, 3, 11, 38, 55, 1, 3, 11, 41, 124, 144, 1, 3, 11, 41, 150, 389, 377, 1, 3, 11, 41, 153, 533, 1187, 987, 1, 3, 11, 41, 153, 568, 1838, 3549, 2584, 1, 3, 11, 41, 153, 571, 2084, 6168, 10447, 6765, 1, 3, 11, 41, 153, 571, 2128

Offset: 1

Author

Clark Kimberling, Mar 14 2012

Keywords

• nonn
• tabl

Comments

Limiting row: A001835

Coefficient of x^n in v(n,x): even-indexed Fibonacci numbers

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

Examples

			First five rows:
1
1...3
1...3...8
1...3...11...21
1...3...11...38...55
First three polynomials v(n,x): 1, 1 + 3x , 1 + 3x + 8x^2.
		

Crossrefs

Cf. 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];
v[n_, x_] := x*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[%]    (* A209759 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209760 *)

Formula

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

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

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