A124804 Number of base 32 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 32, 94, 218, 586, 1562, 4288, 11876, 33250, 93746, 265924, 757976, 2169316, 6229892, 17944006, 51816578, 149965330, 434882642, 1263332452, 3675765416, 10710126976, 31246397456, 91266942586, 266864938646, 781080332332

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, 32) 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,..,32}. 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: A220581 A297730 A360436 * A188184 A126386 A208635

Adjacent sequences: A124801 A124802 A124803 * A124805 A124806 A124807

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved