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 A124843 Number of base 8 circular n-digit numbers with adjacent digits differing by 2 or less. 2

%I #16 Aug 12 2023 13:00:11

%S 1,8,34,122,502,2098,8980,38928,170382,750722,3323554,14763438,

%T 65736004,293186252,1309156946,5850527002,26160514526,117022825786,

%U 523619082772,2343388805944,10488943094022,46952619517170

%N Number of base 8 circular n-digit numbers with adjacent digits differing by 2 or less.

%C [Empirical] a(base,n)=a(base-1,n)+A005191(n+1) for base>=2.int(n/2)+1.

%C See A285280 for confirmation of linear recurrence and code to produce sequence; also confirms conjectured g.f. from _Colin Barker_. - _Ray Chandler_, Aug 12 2023.

%H Ray Chandler, <a href="/A124843/b124843.txt">Table of n, a(n) for n = 0..99</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (8, -15, -10, 29, 4, -12).

%F G.f.: (1 - 15*x^2 - 20*x^3 + 87*x^4 + 16*x^5 - 60*x^6) / ((1 - 3*x - x^2 + 2*x^3)*(1 - 5*x + x^2 + 6*x^3)). - _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]`>2)+(\$[(i+1)mod N]`-\$[i]`>2))

%Y Cf. Row 8 of A285280.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006

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Last modified October 3 22:39 EDT 2023. Contains 365872 sequences. (Running on oeis4.)