cp's OEIS Frontend

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

%I A124999 #14 Apr 30 2025 14:56:46
%S A124999 1,5,23,101,467,2165,10055,46709,216995,1008101,4683383,21757829,
%T A124999 101081459,469599317,2181641639,10135364501,47086382915,218751625157,
%U A124999 1016265649367,4721317472933,21934066839827,101900219778101,473403079631879,2199312977861813
%N A124999 Number of base 5 circular n-digit numbers with adjacent digits differing by 3 or less.
%C A124999 [Empirical] a(base,n)=a(base-1,n)+A025012(n+1) for base>=3.int(n/2)+1
%H A124999 OEIS Wiki, <a href="/wiki/Number_of_base_k_circular_n-digit_numbers_with_adjacent_digits_differing_by_d_or_less">Number of base k circular n-digit numbers with adjacent digits differing by d or less</a>
%F A124999 Conjectures from _Colin Barker_, Jun 02 2017: (Start)
%F A124999 G.f.: (1 - 2*x)*(1 + 2*x + 3*x^2) / ((1 - x)*(1 - 4*x - 3*x^2)).
%F A124999 a(n) = 1 + (2-sqrt(7))^n + (2+sqrt(7))^n for n>0.
%F A124999 a(n) = 5*a(n-1) - a(n-2) - 3*a(n-3) for n>3.
%F A124999 (End)
%o A124999 (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))
%K A124999 nonn,base
%O A124999 0,2
%A A124999 _R. H. Hardin_, Dec 28 2006