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Number of base 8 circular n-digit numbers with adjacent digits differing by 3 or less.
0

%I #11 Jun 03 2017 13:00:17

%S 1,8,44,212,1156,6428,36338,206942,1183164,6777860,38866134,222980282,

%T 1279588414,7343932838,42151639560,241943513252,1388738207756,

%U 7971319975484,45755345035400,262636025020328,1507534275820126

%N Number of base 8 circular n-digit numbers with adjacent digits differing by 3 or less.

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

%F G.f.: (1 - 10*x^2 - 40*x^3 + 45*x^4 + 48*x^5 - 35*x^6 - 12*x^7 + 7*x^8) / ((1 + x)*(1 - 3*x + x^3)*(1 - 6*x + x^2 + 3*x^3 - x^4)) (conjectured). - _Colin Barker_, Jun 03 2017

%o (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 nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006