A124999 Number of base 5 circular n-digit numbers with adjacent digits differing by 3 or less.

1, 5, 23, 101, 467, 2165, 10055, 46709, 216995, 1008101, 4683383, 21757829, 101081459, 469599317, 2181641639, 10135364501, 47086382915, 218751625157, 1016265649367, 4721317472933, 21934066839827, 101900219778101, 473403079631879, 2199312977861813

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+A025012(n+1) for base>=3.int(n/2)+1

Links

Table of n, a(n) for n=0..23.

Formula

Conjectures from Colin Barker, Jun 02 2017: (Start)

G.f.: (1 - 2*x)*(1 + 2*x + 3*x^2) / ((1 - x)*(1 - 4*x - 3*x^2)).

a(n) = 1 + (2-sqrt(7))^n + (2+sqrt(7))^n for n>0.

a(n) = 5*a(n-1) - a(n-2) - 3*a(n-3) for n>3.

(End)

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>3)+($[(i+1)mod N]`-$[i]`>3))

Crossrefs

Sequence in context: A274322 A085350 A113443 * A258431 A356340 A120902

Adjacent sequences: A124996 A124997 A124998 * A125000 A125001 A125002

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved