A208914 Triangle of coefficients of polynomials v(n,x) jointly generated with A208913; see the Formula section.

1, 2, 2, 3, 4, 4, 4, 6, 16, 8, 5, 8, 40, 32, 16, 6, 10, 80, 80, 96, 32, 7, 12, 140, 160, 336, 192, 64, 8, 14, 224, 280, 896, 672, 512, 128, 9, 16, 336, 448, 2016, 1792, 2304, 1024, 256, 10, 18, 480, 672, 4032, 4032, 7680, 4608, 2560, 512, 11, 20, 660, 960

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..59.

Formula

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

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

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

Example

First five rows:
1
2...2
3...4...4
4...6...16...8
5...8...40...32...16
First five polynomials v(n,x):
1
2 + 2x
3 + 4x + 4x^2
4 + 6x + 16x^2 + 8x^3
5 + 8x + 40x^2 + 32x^3 + 16x^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] + 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[%]    (* A208913 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208914 *)

Crossrefs

Cf. A208913, A208510.

Sequence in context: A309559 A130128 A210556 * A049980 A359897 A209698

Adjacent sequences: A208911 A208912 A208913 * A208915 A208916 A208917

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 03 2012

Status

approved