A209170 Triangle of coefficients of polynomials u(n,x) jointly generated with A209171; see the Formula section.

1, 2, 1, 5, 6, 2, 11, 20, 13, 3, 23, 57, 57, 27, 5, 47, 149, 202, 144, 53, 8, 95, 369, 633, 604, 334, 101, 13, 191, 881, 1831, 2192, 1618, 733, 188, 21, 383, 2049, 5007, 7217, 6665, 4022, 1544, 344, 34, 767, 4673, 13135, 22153, 24570, 18519, 9461

Offset

1,2

Comments

Row n ends with A000045 (Fibonacci numbers).

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..52.

Formula

u(n,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
2....1
5....6....2
11...20...13...3
23...57...57...27...5
First three polynomials v(n,x): 1, 2 + x, 5 + 6x + 2x^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] + (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[%]    (* A209170 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209171 *)

Crossrefs

Cf. A209171, A208510.

Sequence in context: A342968 A323312 A231774 * A231732 A185384 A274728

Adjacent sequences: A209167 A209168 A209169 * A209171 A209172 A209173

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 08 2012

Status

approved