cp's OEIS Frontend

A125343 Number of base 6 circular n-digit numbers with adjacent digits differing by 4 or less.

%I A125343 #13 Apr 30 2025 15:09:24
%S A125343 1,6,34,186,1058,6026,34354,195866,1116738,6367146,36302674,206981946,
%T A125343 1180120418,6728529866,38363130994,218729774426,1247101396098,
%U A125343 7110426078186,40540535975314,231144384189306,1317884064847778
%N A125343 Number of base 6 circular n-digit numbers with adjacent digits differing by 4 or less.
%C A125343 [Empirical] a(base,n)=a(base-1,n)+A025014(n+1) for base>=4.int(n/2)+1
%H A125343 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 A125343 Conjectures from _Colin Barker_, Jun 02 2017: (Start)
%F A125343 G.f.: (1 - x^2 - 8*x^3) / ((1 - x)*(1 - 5*x - 4*x^2)).
%F A125343 a(n) = 1 + ((5-sqrt(41))/2)^n + ((5+sqrt(41))/2)^n for n>0.
%F A125343 a(n) = 6*a(n-1) - a(n-2) - 4*a(n-3) for n>3.
%F A125343 (End)
%o A125343 (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>4)+($[(i+1)mod N]`-$[i]`>4))
%K A125343 nonn,base
%O A125343 0,2
%A A125343 _R. H. Hardin_, Dec 28 2006