A209570 Triangle of coefficients of polynomials v(n,x) jointly generated with A209569; see the Formula section.

1, 2, 2, 3, 4, 2, 4, 8, 8, 2, 5, 14, 20, 12, 2, 6, 22, 42, 40, 16, 2, 7, 32, 78, 102, 68, 20, 2, 8, 44, 132, 222, 210, 104, 24, 2, 9, 58, 208, 432, 534, 382, 148, 28, 2, 10, 74, 310, 772, 1188, 1126, 634, 200, 32, 2, 11, 92, 442, 1290, 2392, 2848, 2142, 982

Offset

1,2

Comments

For n>1, row n begins and ends with 2.

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

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

Links

Table of n, a(n) for n=1..63.

Formula

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

v(n,x)=2x*u(n-1,x)+v(n-1,x) +1,

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

Example

First five rows:
1
2...2
3...4....2
4...8....8....2
5...14...20...12...2
First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 2x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, 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[%]   (* A209569 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209570 *)

Crossrefs

Cf. A209569, A208510.

Sequence in context: A143595 A211702 A208521 * A205703 A363100 A367467

Adjacent sequences: A209567 A209568 A209569 * A209571 A209572 A209573

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved