A209164 Triangle of coefficients of polynomials u(n,x) jointly generated with A209165; see the Formula section.

1, 2, 1, 5, 5, 1, 11, 15, 6, 1, 23, 41, 27, 9, 1, 47, 105, 95, 45, 10, 1, 95, 257, 295, 185, 65, 13, 1, 191, 609, 847, 665, 315, 91, 14, 1, 383, 1409, 2303, 2177, 1295, 497, 119, 17, 1, 767, 3201, 6015, 6657, 4767, 2289, 735, 153, 18, 1, 1535, 7169, 15231

Offset

1,2

Comments

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

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

Links

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

Formula

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

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

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

Example

First five rows:
1
2....1
5....5....1
11...15...6....1
23...41...27...9...1
First three polynomials v(n,x): 1, 2 + x, 5 + 5x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := (x + 1)*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[%]    (* A209164 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209165 *)

Crossrefs

Cf. A209165, A208510.

Sequence in context: A126350 A204111 A079502 * A209148 A126124 A123971

Adjacent sequences: A209161 A209162 A209163 * A209165 A209166 A209167

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 08 2012

Status

approved