A124706 Number of base 13 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 13, 37, 85, 225, 593, 1609, 4409, 12217, 34105, 95817, 270569, 767325, 2184013, 6235693, 17852045, 51229417, 147318953, 424429081, 1224825209, 3539918965, 10244733605, 29685367573, 86113604309, 250061941093, 726831403493

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, 13) 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,..,13}. 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..25.

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: A157837 A039367 A139697 * A145990 A089528 A317986

Adjacent sequences: A124703 A124704 A124705 * A124707 A124708 A124709

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved