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

1,3

Links

Table of n, a(n) for n=1..73.

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.

Example

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

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 *)

Crossrefs

Cf. A208514.

Sequence in context: A209435 A263744 A268956 * A286880 A178030 A131879

Adjacent sequences: A208512 A208513 A208514 * A208516 A208517 A208518

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 28 2012

Status

approved