A124713 Number of base 20 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 20, 58, 134, 358, 950, 2596, 7160, 19966, 56078, 158488, 450140, 1283848, 3674600, 10549282, 30365294, 87605806, 253263470, 733498744, 2127803180, 6181574548, 17982188708, 52373316262, 152706201170, 445700295760

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, 20) 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,..,20}. 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: A297397 A104100 A069132 * A126374 A229536 A220013

Adjacent sequences: A124710 A124711 A124712 * A124714 A124715 A124716

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved