A124709 Number of base 16 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 16, 46, 106, 282, 746, 2032, 5588, 15538, 43522, 122676, 347528, 988692, 2822836, 8084374, 23214866, 66819298, 192723746, 556887508, 1611815768, 4672057072, 13560785792, 39408774154, 114653288678, 333906950236

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, 16) 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,..,16}. 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: A235555 A069128 A099003 * A244094 A235549 A126370

Adjacent sequences: A124706 A124707 A124708 * A124710 A124711 A124712

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved