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%I #21 Sep 11 2018 03:03:47
%S 1,2,3,5,10,15,25,50,75,125,250,375,625,1250,1875,3125,6250,9375,
%T 15625,31250,46875,78125,156250,234375,390625,781250,1171875,1953125,
%U 3906250,5859375,9765625,19531250,29296875,48828125,97656250,146484375,244140625,488281250
%N a(3*n) = 3*a(3*n-1)-3*a(3*n-2)+2*a(3*n-3), a(3*n+1) = 3*a(3*n)-3*a(3*n-1)+2*a(3*n-2), a(3*n+2) = 3*a(3*n+1)-3*a(3*n) with a(0)=1, a(1)=2, a(2)=3.
%C a(0) = 1, a(1) = 2, for n >= 3: a(n-1) < a(n) = natural numbers such that (a(n-2)+a(n-1)+a(n))*a(n-1)/(a(n-2)*a(n)) are integers m > 1. Corresponding values of m for n>=3: 4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,... a(3*k) = a(3*k-1) + a(3*k-2), a(3*k+1) = 2*a(3*k), a(3*k+2) = a(3*k+1) + a(3*k) for k >= 1. [_Jaroslav Krizek_, Nov 26 2009]
%H D. Panario, M. Sahin, Q. Wang, <a href="http://www.emis.de/journals/INTEGERS/papers/n78/n78.Abstract.html">A family of Fibonacci-like conditional sequences</a>, INTEGERS, Vol. 13, 2013, #A78.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,5).
%F a(n) = 5*a(n-3). G.f.: -(3*x^2+2*x+1)/(5*x^3-1). [_Colin Barker_, Oct 11 2012]
%t RecurrenceTable[{a[0]== 1, a[1]==2, a[2] == 3, a[n]== 5 a[n-3]}, a, {n, 40}] (* _Vincenzo Librandi_, Sep 11 2018 *)
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Oct 19 2007
%E More terms after a(14) by _Jaroslav Krizek_, Nov 26 2009
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