A124858 Number of base 12 circular n-digit numbers with adjacent digits differing by 2 or less.

1, 12, 54, 198, 842, 3622, 15984, 71468, 323042, 1472022, 6751064, 31123148, 144092684, 669468708, 3119587196, 14572658668, 68216250402, 319893194558, 1502357897232, 7064711394284, 33257109397452, 156701323391972

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+A005191(n+1) for base>=2.int(n/2)+1.

See A285280 for confirmation of linear recurrence and code to produce sequence. - Ray Chandler, Aug 12 2023.

Links

Ray Chandler, Table of n, a(n) for n = 0..99

OEIS Wiki, Number of base k circular n-digit numbers with adjacent digits differing by d or less

Index entries for linear recurrences with constant coefficients, signature (12, -45, 30, 134, -160, -141, 170, 59, -60, -9, 6).

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>2)+($[(i+1)mod N]`-$[i]`>2))
(PARI) Vec((-1+45*x^2-60*x^3-402*x^4+640*x^5+705*x^6-1020*x^7-413*x^8+480*x^9+81*x^10-60*x^11)/((1-5*x+2*x^2+9*x^3-3*x^4-3*x^5)*(1-7*x+8*x^2+15*x^3-9*x^4-5*x^5+2*x^6))+O(x^99)) \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. Row 12 of A285280.

Cf. A005191.

Sequence in context: A019582 A025204 A005549 * A183713 A126399 A137938

Adjacent sequences: A124855 A124856 A124857 * A124859 A124860 A124861

Keyword

nonn,base,easy

Author

R. H. Hardin, Dec 28 2006

Status

approved