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

1, 2, 2, 3, 5, 4, 4, 10, 14, 8, 5, 17, 34, 36, 16, 6, 26, 68, 104, 88, 32, 7, 37, 120, 240, 296, 208, 64, 8, 50, 194, 480, 776, 800, 480, 128, 9, 65, 294, 868, 1736, 2352, 2080, 1088, 256, 10, 82, 424, 1456, 3472, 5824, 6784, 5248, 2432, 512, 11, 101, 588

Offset

1,2

Comments

Column 1: 1,2,3,4,5,6,7,8,...

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

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

Alternating row sums: 1,0,2,0,2,0,2,0,2,0,2,0,...

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
2...2
3...5....4
4...10...14...8
5...17...34...36...16
First three polynomials v(n,x): 1, 2 + 2x , 3 + 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. A209761, A208510.

Sequence in context: A210554 A208912 A210212 * A026408 A301790 A301964

Adjacent sequences: A209759 A209760 A209761 * A209763 A209764 A209765

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 14 2012

Status

approved