A124851 Number of base 9 circular n-digit numbers with adjacent digits differing by 2 or less.

1, 9, 39, 141, 587, 2479, 10731, 47063, 208547, 931047, 4180239, 18849103, 85269011, 386687375, 1756855951, 7993210831, 36405316227, 165940691695, 756832203759, 3453347063599, 15762537566627, 71964915505967

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 (9, -21, -7, 50, -4, -30, 4, 4).

Crossrefs

Cf. Row 9 of A285280.

Formula

G.f.: (1 - 21*x^2 - 14*x^3 + 150*x^4 - 16*x^5 - 150*x^6 + 24*x^7 + 28*x^8) / ((1 + x)*(1 - 4*x + 2*x^2)*(1 - 6*x + 5*x^2 + 8*x^3 - 4*x^4 - 2*x^5)). - Colin Barker, Jun 02 2017