A124719 Number of base 26 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 26, 76, 176, 472, 1256, 3442, 9518, 26608, 74912, 212206, 604058, 1726582, 4952246, 14246644, 41090936, 118785568, 344073056, 998415598, 2901784298, 8445850762, 24614293082, 71820129424, 209785569908, 613390314046

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, 26) 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,..,26}. 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: A304657 A262221 A139698 * A126380 A083578 A173307

Adjacent sequences: A124716 A124717 A124718 * A124720 A124721 A124722

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved