A209151 Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section.

1, 2, 1, 3, 4, 2, 4, 8, 8, 3, 5, 13, 19, 15, 5, 6, 19, 36, 42, 28, 8, 7, 26, 60, 91, 89, 51, 13, 8, 34, 92, 170, 216, 182, 92, 21, 9, 43, 133, 288, 446, 489, 363, 164, 34, 10, 53, 184, 455, 826, 1105, 1068, 709, 290, 55, 11, 64, 246, 682, 1414, 2219, 2619

Offset

1,2

Comments

Last term in each row is a Fibonacci number (A000045).

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

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

Links

Table of n, a(n) for n=1..62.

Formula

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

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

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

Example

First five rows:
1
2...1
3...4....2
4...8....8....3
5...13...19...15...5
First three polynomials v(n,x): 1, 2 + x, 3 + 4x + 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*u[n - 1, x] + 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[%]    (* A209151 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208337 *)

Crossrefs

Cf. A208337, A208510.

Sequence in context: A131389 A131394 A130585 * A125100 A128544 A120058

Adjacent sequences: A209148 A209149 A209150 * A209152 A209153 A209154

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 07 2012

Status

approved