A124843 Number of base 8 circular n-digit numbers with adjacent digits differing by 2 or less.

1, 8, 34, 122, 502, 2098, 8980, 38928, 170382, 750722, 3323554, 14763438, 65736004, 293186252, 1309156946, 5850527002, 26160514526, 117022825786, 523619082772, 2343388805944, 10488943094022, 46952619517170

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 (8, -15, -10, 29, 4, -12).

Crossrefs

Cf. Row 8 of A285280.

Formula

G.f.: (1 - 15*x^2 - 20*x^3 + 87*x^4 + 16*x^5 - 60*x^6) / ((1 - 3*x - x^2 + 2*x^3)*(1 - 5*x + x^2 + 6*x^3)). - Colin Barker, Jun 03 2017