OFFSET
0,2
COMMENTS
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]
LINKS
D. Panario, M. Sahin, Q. Wang, A family of Fibonacci-like conditional sequences, INTEGERS, Vol. 13, 2013, #A78.
Index entries for linear recurrences with constant coefficients, signature (0,0,5).
FORMULA
a(n) = 5*a(n-3). G.f.: -(3*x^2+2*x+1)/(5*x^3-1). [Colin Barker, Oct 11 2012]
MATHEMATICA
RecurrenceTable[{a[0]== 1, a[1]==2, a[2] == 3, a[n]== 5 a[n-3]}, a, {n, 40}] (* Vincenzo Librandi, Sep 11 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Oct 19 2007
EXTENSIONS
More terms after a(14) by Jaroslav Krizek, Nov 26 2009
STATUS
approved