A124783 Number of base 28 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 28, 82, 190, 510, 1358, 3724, 10304, 28822, 81190, 230112, 655364, 1874160, 5378128, 15479098, 44666150, 129178822, 374342918, 1086721216, 3159778004, 9200609500, 26824994540, 78302400478, 228812026154, 669286986808

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, 28) 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,..,28}. 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: A039415 A043238 A044018 * A126382 A165009 A179790

Adjacent sequences: A124780 A124781 A124782 * A124784 A124785 A124786

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved