A073300 If n=pqr...st in ternary, a(n)=value of the continuant [p,q,r,...,s,t].

1, 1, 2, 1, 2, 3, 1, 3, 5, 1, 2, 3, 1, 3, 5, 1, 4, 7, 2, 3, 4, 2, 5, 8, 2, 7, 12, 1, 2, 3, 1, 3, 5, 1, 4, 7, 2, 3, 4, 2, 5, 8, 2, 7, 12, 3, 4, 5, 3, 7, 11, 3, 10, 17, 1, 3, 5, 1, 4, 7, 1, 5, 9, 3, 5, 7, 3, 8, 13, 3, 11, 19, 5, 7, 9, 5, 12, 19, 5, 17, 29, 1, 2, 3, 1, 3, 5, 1, 4, 7, 2, 3, 4, 2, 5, 8, 2, 7

Offset

0,3

Comments

The continuant function is defined in A072347. The successive record values in this sequence occur at n=0,2,5,8 and, for k>=3, at n=3^k-3^(k-1)-1, 3^k-3^(k-2)-1 and 3^k-1 and are given in A073301.

a(3^n-1) = A000129(n+1) for n>=0. - Alois P. Heinz, Aug 06 2013

Links

Alois P. Heinz, Table of n, a(n) for n = 0..6560 (6560 = 3^8-1)

Wikipedia, Continuant

Maple

c:= proc() option remember;
      if nargs=0 then 1
    elif nargs=1 then args[1]
    else args[-1]*c(seq(args[i], i=1..nargs-1))
                 +c(seq(args[i], i=1..nargs-2))
      fi
    end:
a:= n-> `if`(n=0, 1, c(convert(n, base, 3)[])):
seq(a(n), n=0..120);  # Alois P. Heinz, Aug 06 2013

Crossrefs

Cf. A072347.

Sequence in context: A091438 A011794 A221640 * A104468 A293003 A110062

Adjacent sequences: A073297 A073298 A073299 * A073301 A073302 A073303

Keyword

base,nonn,look

Author

John W. Layman, Jul 23 2002

Status

approved