A124852 Number of base 10 circular n-digit numbers with adjacent digits differing by 2 or less.

1, 10, 44, 160, 672, 2860, 12482, 55198, 246712, 1111372, 5037174, 22940158, 104870790, 480863770, 2210197754, 10178143810, 46942294232, 216761695840, 1001878336772, 4634206919128, 21448419453382, 99316222901062

Offset: 0

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base

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; also confirms conjectured g.f. from Colin Barker. - 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 (11, -39, 39, 37, -65, 4, 16, -1, -1).

Crossrefs

Cf. Row 10 of A285280.

Formula

G.f.: (1 - x - 27*x^2 + 27*x^3 + 201*x^4 - 313*x^5 + 8*x^6 + 112*x^7 - 7*x^8 - 9*x^9) / ((1 - x)*(1 + x)*(1 - 4*x + x^2 + x^3)*(1 - 7*x + 11*x^2 - x^4)). - Colin Barker, Jun 01 2017