A209688 Triangle of coefficients of polynomials v(n,x) jointly generated with A115241; see the Formula section.

1, 3, 4, 2, 5, 5, 2, 6, 9, 7, 2, 7, 14, 16, 9, 2, 8, 20, 30, 25, 11, 2, 9, 27, 50, 55, 36, 13, 2, 10, 35, 77, 105, 91, 49, 15, 2, 11, 44, 112, 182, 196, 140, 64, 17, 2, 12, 54, 156, 294, 378, 336, 204, 81, 19, 2, 13, 65, 210, 450, 672, 714, 540, 285, 100, 21, 2

Offset

1,2

Comments

Alternating row sums: 1,3,2,2,2,2,2,2,2,2,2,2,...

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

Links

Table of n, a(n) for n=1..67.

Formula

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

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

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

Example

First five rows:
1
3...1
4...2...3
5...5...2
6...9...7...2
First three polynomials v(n,x): 1, 3 + x , 4 + 2x + 3x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, 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[%]    (* A115241 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209688 *)

Crossrefs

Cf. A115241, A208510.

Sequence in context: A246832 A133570 A117041 * A143939 A197269 A201905

Adjacent sequences: A209685 A209686 A209687 * A209689 A209690 A209691

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 12 2012

Status

approved