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A073300 If n=pqr...st in ternary, a(n)=value of the continuant [p,q,r,...,s,t]. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 16 04:36 EDT 2021. Contains 343030 sequences. (Running on oeis4.)