A209775 Triangle of coefficients of polynomials u(n,x) jointly generated with A209776; see the Formula section.

1, 1, 2, 3, 6, 4, 5, 16, 18, 8, 9, 36, 60, 48, 16, 15, 76, 166, 194, 120, 32, 25, 152, 414, 634, 572, 288, 64, 41, 294, 960, 1822, 2154, 1584, 672, 128, 67, 554, 2114, 4790, 7004, 6752, 4192, 1536, 256, 109, 1024, 4476, 11800, 20560, 24498, 19952

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..52.

Formula

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

v(n,x)=(x+1)*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
3...6....4
5...16...18...8
9...36...60...48...16
First three polynomials u(n,x): 1, 1 + 2x, 3 + 6x + 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 + 1)*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[%]    (* A209775 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209776 *)

Crossrefs

Cf. A209776, A208510.

Sequence in context: A072637 A138153 A353590 * A360599 A306231 A125703

Adjacent sequences: A209772 A209773 A209774 * A209776 A209777 A209778

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 15 2012

Status

approved