[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A124709
Number of base 16 circular n-digit numbers with adjacent digits differing by 1 or less.
0
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
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
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 28 2006
STATUS
approved