A052133 CONTINUANT transform of 0, 1, 1, 2, 1, 3, 2, 3, ... (A002487).

0, 1, 1, 3, 4, 15, 34, 117, 151, 721, 2314, 12291, 26896, 146771, 467209, 2015607, 2482816, 14429687, 60201564, 435840635, 1367723469, 11377628387, 58255865404, 419168686215, 896593237834, 6695321351053, 34373199993099, 281680921295845, 879415963880634

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

N. J. A. Sloane, Transforms

Maple

b:= proc(n) option remember; `if`(n<2, n,
      `if`(irem(n, 2, 'r')=0, b(r), b(r) + b(r+1)))
    end:
a:= proc(n) option remember; `if`(n<-1, 0,
      `if`(n<0, 1, b(n)*a(n-1)+a(n-2)))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Aug 06 2013

Mathematica

b[n_] := b[n] = If[n < 2, n, {q, r} = QuotientRemainder[n, 2]; If[r == 0, b[q], b[q] + b[q+1]]]; a[n_] := a[n] = If[n < -1, 0, If[n < 0, 1, b[n]*a[n-1] + a[n-2]]]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Nov 25 2014, after Alois P. Heinz *)

Crossrefs

Cf. A071898.

Sequence in context: A344261 A055486 A041665 * A332051 A209479 A209338

Adjacent sequences: A052130 A052131 A052132 * A052134 A052135 A052136

Keyword

nonn

Author

N. J. A. Sloane, Jul 18 2002

Status

approved