A249131 p(1,n), where the polynomial p(n,x) is defined in Comments; sum of the numbers in row n of the triangular array at A249130.

1, 3, 5, 17, 37, 139, 361, 1473, 4361, 19091, 62701, 291793, 1044205, 5129307, 19748177, 101817089, 417787921, 2250495523, 9770678101, 54780588561, 250194150581, 1455367098923, 6959638411705, 41888448785857, 208919770666777, 1298019439099059

Offset

0,2

Comments

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + 2*floor((n+1)/2)/f(n-1,x), where f(0,x) = 1.

Links

Table of n, a(n) for n=0..25.

Example

The first 3 rows of the array at A249130:
  1
  2    1
  2    2    1,
so that the first 3 terms of A249131 are 1,3,5.

Mathematica

z = 15; p[x_, n_] := x + 2 Floor[n/2]/p[x, n - 1]; p[x_, 1] = 1;
t = Table[Factor[p[x, n]], {n, 1, z}]
u = Numerator[t]
TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249130 array *)
u /. x -> 1  (* A249131 *)

Crossrefs

Cf. A249130.

Sequence in context: A305411 A019414 A350905 * A260406 A081762 A148515

Adjacent sequences: A249128 A249129 A249130 * A249132 A249133 A249134

Keyword

nonn,easy,changed

Author

Clark Kimberling, Oct 22 2014

Status

approved