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

1, 1, 4, 1, 4, 12, 1, 4, 16, 40, 1, 4, 20, 64, 128, 1, 4, 24, 88, 240, 416, 1, 4, 28, 112, 368, 896, 1344, 1, 4, 32, 136, 512, 1504, 3264, 4352, 1, 4, 36, 160, 672, 2240, 5952, 11776, 14080, 1, 4, 40, 184, 848, 3104, 9472, 23168, 41984, 45568, 1, 4, 44

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...4
1...4...12
1...4...16...40
1...4...20...64...128
First five polynomials v(n,x):
1
1 + 4x
1 + 4x + 12x^2
1 + 4x + 16x^2 + 40x^3
1 + 4x + 20x^2 + 64x^3 + 128x^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. A208917, A208510.

Sequence in context: A209576 A055886 A132478 * A228782 A205125 A248978

Adjacent sequences: A208915 A208916 A208917 * A208919 A208920 A208921

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 04 2012

Status

approved