A124828 Number of base 7 circular n-digit numbers with adjacent digits differing by 2 or less.

1, 7, 29, 103, 417, 1717, 7229, 30793, 132225, 570649, 2470769, 10719793, 46569777, 202477633, 880792193, 3832748833, 16681516545, 72613292353, 316105114817, 1376159456641, 5991281182977, 26084303730049

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 (7, -10, -10, 14, 4, -4).

Crossrefs

Cf. Row 7 of A285280.

Formula

G.f.: (1 - 10*x^2 - 20*x^3 + 42*x^4 + 16*x^5 - 20*x^6) / ((1 - x)*(1 - 2*x - 2*x^2)*(1 - 4*x - 2*x^2 + 2*x^3)). - Colin Barker, Jun 03 2017