A124717 Number of base 24 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 24, 70, 162, 434, 1154, 3160, 8732, 24394, 68634, 194300, 552752, 1579004, 4526364, 13014190, 37515722, 108392314, 313803194, 910109980, 2643790592, 7691092024, 22403591624, 65337858370, 190759113662, 557493641284

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1

a(n) = T(n, 24) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,24}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

Table of n, a(n) for n=0..24.

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>1)+($[(i+1)mod N]`-$[i]`>1))

Crossrefs

Sequence in context: A304157 A051876 A069174 * A126378 A342800 A320702

Adjacent sequences: A124714 A124715 A124716 * A124718 A124719 A124720

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved