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 A125343 Number of base 6 circular n-digit numbers with adjacent digits differing by 4 or less. 0

%I

%S 1,6,34,186,1058,6026,34354,195866,1116738,6367146,36302674,206981946,

%T 1180120418,6728529866,38363130994,218729774426,1247101396098,

%U 7110426078186,40540535975314,231144384189306,1317884064847778

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

%C [Empirical] a(base,n)=a(base-1,n)+A025014(n+1) for base>=4.int(n/2)+1

%F Conjectures from _Colin Barker_, Jun 02 2017: (Start)

%F G.f.: (1 - x^2 - 8*x^3) / ((1 - x)*(1 - 5*x - 4*x^2)).

%F a(n) = 1 + ((5-sqrt(41))/2)^n + ((5+sqrt(41))/2)^n for n>0.

%F a(n) = 6*a(n-1) - a(n-2) - 4*a(n-3) for n>3.

%F (End)

%o (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 nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006

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Last modified January 31 18:34 EST 2023. Contains 359980 sequences. (Running on oeis4.)