A208917 Triangle of coefficients of polynomials u(n,x) jointly generated with A208918; see the Formula section.

1, 1, 2, 1, 4, 8, 1, 6, 16, 24, 1, 8, 24, 56, 80, 1, 10, 32, 96, 208, 256, 1, 12, 40, 144, 384, 736, 832, 1, 14, 48, 200, 608, 1472, 2624, 2688, 1, 16, 56, 264, 880, 2496, 5632, 9216, 8704, 1, 18, 64, 336, 1200, 3840, 10112, 21120, 32256, 28160, 1, 20, 72

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..58.

Formula

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

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

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

Example

First five rows:
1
1...2
1...4...8
1...6...16...24
1...8...24...56...80
First five polynomials u(n,x):
1
1 + 2x
1 + 4x + 8x^2
1 + 6x + 16x^2 + 24x^3
1 + 8x + 24x^2 + 56x^3 + 80x^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] + 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[%]    (* A208917 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208918 *)

Crossrefs

Cf. A208918, A208510.

Sequence in context: A038557 A348678 A011234 * A161381 A220579 A330787

Adjacent sequences: A208914 A208915 A208916 * A208918 A208919 A208920

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 04 2012

Status

approved