A208660 Triangle of coefficients of polynomials u(n,x) jointly generated with A208904; see the Formula section.

1, 1, 2, 1, 8, 2, 1, 18, 14, 2, 1, 32, 52, 20, 2, 1, 50, 140, 104, 26, 2, 1, 72, 310, 380, 174, 32, 2, 1, 98, 602, 1106, 806, 262, 38, 2, 1, 128, 1064, 2744, 2924, 1472, 368, 44, 2, 1, 162, 1752, 6048, 8892, 6412, 2432, 492, 50, 2, 1, 200, 2730, 12168, 23652

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

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

Example

First five rows:
1
1...2
1...8....2
1...18...14...2
1...32...52...20...2
First five polynomials u(n,x):
1
1 + 2x
1 + 8x + 2x^2
1 + 18x + 14x^2 + 2x^3
1 + 32x + 52x^2 + 20x^3 + 2x^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_] := u[n - 1, x] + (x + 1)*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[%]    (* A208660 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208904 *)

Crossrefs

Cf. A208904, A208510.

Sequence in context: A118961 A180956 A208921 * A367024 A114706 A046740

Adjacent sequences: A208657 A208658 A208659 * A208661 A208662 A208663

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 03 2012

Status

approved