A208915 Triangle of coefficients of polynomials u(n,x) jointly generated with A208916; see the Formula section.

1, 1, 2, 1, 4, 6, 1, 6, 12, 14, 1, 8, 18, 36, 38, 1, 10, 24, 66, 108, 94, 1, 12, 30, 104, 210, 308, 246, 1, 14, 36, 150, 344, 674, 892, 622, 1, 16, 42, 204, 510, 1224, 2098, 2500, 1606, 1, 18, 48, 266, 708, 1990, 4024, 6402, 7052, 4094, 1, 20, 54, 336, 938

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..60.

Formula

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

v(n,x)=2x*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...4...6
1...6...12...14
1...8...18...36...38
First five polynomials u(n,x):
1
1 + 2x
1 + 4x + 6x^2
1 + 6x + 12x^2 + 14x^3
1 + 8x + 18x^2 + 36x^3 + 38x^4

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := 2 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[%]    (* A208915 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208916 *)

Crossrefs

Cf. A208914, A208510.

Sequence in context: A063872 A199909 A033884 * A199704 A062344 A208759

Adjacent sequences: A208912 A208913 A208914 * A208916 A208917 A208918

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 03 2012

Status

approved