A124705 Number of base 12 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 12, 34, 78, 206, 542, 1468, 4016, 11110, 30966, 86864, 244916, 693536, 1971072, 5619466, 16064438, 46032790, 132184022, 380276272, 1095828356, 3162539596, 9139382876, 26444232046, 76600376186, 222113604712, 644654567192

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, 12) 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,..,12}. 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 - 55*x^2 + 220*x^3 - 135*x^4 - 672*x^5 + 1050*x^6 + 216*x^7 - 1015*x^8 + 160*x^9 + 270*x^10 - 40*x^11 - 11*x^12) / ((1 - 5*x + 5*x^2 + 6*x^3 - 7*x^4 - 2*x^5 + x^6)*(1 - 7*x + 15*x^2 - 6*x^3 - 11*x^4 + 6*x^5 + x^6)) (conjectured). - Colin Barker, Jul 17 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: A069125 A142245 A139635 * A296154 A126366 A199114

Adjacent sequences: A124702 A124703 A124704 * A124706 A124707 A124708

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved