A124803 Number of base 31 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 31, 91, 211, 567, 1511, 4147, 11483, 32143, 90607, 256971, 732323, 2095527, 6016951, 17327779, 50028971, 144768703, 419747711, 1219179643, 3546768563, 10332747607, 30141046727, 88025807059, 257351710523, 753131995951

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, 31) 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,..,31}. 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: A359650 A360488 A139700 * A126385 A061155 A098440

Adjacent sequences: A124800 A124801 A124802 * A124804 A124805 A124806

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved