A209761 Triangle of coefficients of polynomials u(n,x) jointly generated with A209762; see the Formula section.

1, 1, 2, 2, 5, 4, 3, 10, 14, 8, 4, 17, 34, 36, 16, 5, 26, 68, 104, 88, 32, 6, 37, 120, 240, 296, 208, 64, 7, 50, 194, 480, 776, 800, 480, 128, 8, 65, 294, 868, 1736, 2352, 2080, 1088, 256, 9, 82, 424, 1456, 3472, 5824, 6784, 5248, 2432, 512, 10, 101, 588

Offset

1,3

Comments

Column 1: 1,1,2,3,4,5,6,7,...

Column 2: 1+1, 1+2^2, 1+3^2, 1+4^2,...

Last term in row n: 2^(n-1)

Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...; A033999

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

Links

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

Formula

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

v(n,x)=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
2...5....4
3...10...14...8
4...17...34...36...16
First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 4x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 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[%]    (* A209761 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209762 *)

Crossrefs

Cf. A209762, A208510.

Sequence in context: A275381 A283235 A209763 * A228526 A209745 A249620

Adjacent sequences: A209758 A209759 A209760 * A209762 A209763 A209764

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 14 2012

Status

approved