A208527 Triangle of coefficients of polynomials v(n,x) jointly generated with A208526; see the Formula section.

1, 1, 4, 1, 4, 10, 1, 4, 12, 28, 1, 4, 14, 40, 76, 1, 4, 16, 52, 124, 208, 1, 4, 18, 64, 176, 384, 568, 1, 4, 20, 76, 232, 592, 1168, 1552, 1, 4, 22, 88, 292, 832, 1936, 3520, 4240, 1, 4, 24, 100, 356, 1104, 2880, 6240, 10512, 11584, 1, 4, 26, 112, 424, 1408

Offset

1,3

Links

Table of n, a(n) for n=1..61.

Formula

u(n,x)=u(n-1,x)+x*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...10
1...4...12...28
1...4...14...40...76
First five polynomials v(n,x):
1
1 + 4x
1 + 4x + 10x^2
1 + 4x + 12x^2 + 28x^3
1 + 4x + 14x^2 + 40x^3 + 76x^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_] := 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[%]  (* A208526 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208527 *)

Crossrefs

Cf. A208526.

Sequence in context: A344685 A201286 A347221 * A209576 A055886 A132478

Adjacent sequences: A208524 A208525 A208526 * A208528 A208529 A208530

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 29 2012

Status

approved