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A125370 Number of base 7 circular n-digit numbers with adjacent digits differing by 5 or less. 0

%I

%S 1,7,47,307,2067,13927,93887,632947,4267107,28767367,193939727,

%T 1307475187,8814549747,59424674407,400620795167,2700848143027,

%U 18208192833987,122753397719047,827561350484207,5579135091500467

%N Number of base 7 circular n-digit numbers with adjacent digits differing by 5 or less.

%C [Empirical] a(base,n)=a(base-1,n)+F(5) for base>=5.int(n/2)+1 and F(d) is the largest coefficient in (1+x+...+x^(2d))^n

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

%F G.f.: (1 - x^2 - 10*x^3) / ((1 - x)*(1 - 6*x - 5*x^2)).

%F a(n) = 1 + (3-sqrt(14))^n + (3+sqrt(14))^n for n>0.

%F a(n) = 7*a(n-1) - a(n-2) - 5*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]`-$[(i+1)mod N]`>5)+($[(i+1)mod N]`-$[i]`>5))

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006

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Last modified January 28 08:20 EST 2023. Contains 359850 sequences. (Running on oeis4.)