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

0,2

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; 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

Index entries for linear recurrences with constant coefficients, signature (7, -10, -10, 14, 4, -4).

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

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))

Crossrefs

Cf. Row 7 of A285280.

Sequence in context: A102485 A246038 A049349 * A296646 A037094 A118171

Adjacent sequences: A124825 A124826 A124827 * A124829 A124830 A124831

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved