A124714 Number of base 21 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 21, 61, 141, 377, 1001, 2737, 7553, 21073, 59217, 167441, 475793, 1357637, 3887541, 11165509, 32152901, 92802433, 268398401, 777651553, 2256800033, 6558953917, 19087539437, 55614451789, 162219429293, 473648632141

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, 21) 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,..,21}. 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: A219690 A325319 A069133 * A126375 A146468 A081302

Adjacent sequences: A124711 A124712 A124713 * A124715 A124716 A124717

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved