cp's OEIS Frontend

A126504 Number of base 9 n-digit numbers with adjacent digits differing by four or less.

%I A126504 #11 Jun 01 2017 12:06:33
%S A126504 1,9,61,429,3011,21141,148433,1042167,7317185,51374875,360709449,
%T A126504 2532586341,17781606753,124846894103,876565722303,6154478019155,
%U A126504 43211363078111,303392406838867,2130156189729353,14956094122197975
%N A126504 Number of base 9 n-digit numbers with adjacent digits differing by four or less.
%C A126504 [Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4.
%F A126504 Conjectures from _Colin Barker_, Jun 01 2017: (Start)
%F A126504 G.f.: (1 - x)*(1 + 3*x - x^3) / (1 - 7*x - x^2 + 6*x^3 - x^5).
%F A126504 a(n) = 7*a(n-1) + a(n-2) - 6*a(n-3) + a(n-5) for n>5.
%F A126504 (End)
%o A126504 (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>4)+($[i+1]`-$[i]`>4))
%Y A126504 Cf. Base 9 differing by three or less A126477, two or less A126396, one or less A126363.
%K A126504 nonn,base
%O A126504 0,2
%A A126504 _R. H. Hardin_, Dec 28 2006