A208515 Triangle of coefficients of polynomials v(n,x) jointly generated with A208514; see the Formula section.

1, 1, 2, 1, 2, 3, 1, 2, 4, 5, 1, 2, 5, 8, 8, 1, 2, 6, 11, 15, 13, 1, 2, 7, 14, 23, 28, 21, 1, 2, 8, 17, 32, 47, 51, 34, 1, 2, 9, 20, 42, 70, 93, 92, 55, 1, 2, 10, 23, 53, 97, 148, 181, 164, 89, 1, 2, 11, 26, 65, 128, 217, 306, 346, 290, 144, 1, 2, 12, 29, 78, 163, 301

Offset: 1

Author

Clark Kimberling, Feb 28 2012

Keywords

• nonn
• tabl

Examples

			First five rows:
1
1...2
1...2...3
1...2...4...5
1...2...5...8...8
First five polynomials v(n,x):
1
1 + 2x
1 + 2x + 3x^2
1 + 2x + 4x^2 + 5x^3
1 + 2x + 5x^2 + 8x^3 + 8x^4
		

Crossrefs

Cf. A208514.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := x*u[n - 1, x] + 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[%]    (* A208514 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208515 *)

Formula

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

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

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