A124784 Number of base 29 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 29, 85, 197, 529, 1409, 3865, 10697, 29929, 84329, 239065, 681017, 1947949, 5591069, 16095325, 46453757, 134375449, 389477849, 1130874025, 3288774857, 9577988869, 27930345269, 81543536005, 238325254277, 697235323189

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, 29) 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,..,29}. 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: A273362 A195314 A323218 * A126383 A032508 A042654

Adjacent sequences: A124781 A124782 A124783 * A124785 A124786 A124787

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved