A124704 Number of base 11 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 11, 31, 71, 187, 491, 1327, 3623, 10003, 27827, 77911, 219263, 619747, 1758131, 5003239, 14276831, 40836163, 117049091, 336123463, 966831503, 2785160227, 8034032147, 23203096519, 67087148063, 194165268355, 562477731491

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, 11) 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,..,11}. 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..25.

Formula

G.f.: (1 - 45*x^2 + 150*x^3 - 18*x^4 - 504*x^5 + 490*x^6 + 300*x^7 - 420*x^8 - 32*x^9 + 72*x^10) / ((1 - x)*(1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 4*x + 2*x^2 + 4*x^3 - 2*x^4)) (conjectured). - Colin Barker, Jun 03 2017

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: A141884 A139634 A173803 * A293659 A089346 A296969

Adjacent sequences: A124701 A124702 A124703 * A124705 A124706 A124707

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved