OFFSET
0,1
COMMENTS
The "Pisano" periods, i.e., the periods of this sequence mod n, begin: 1, 6, 8, 6, 20, 24, 16, 12, 24, 60, 5, 24, ..., a sequence which is not in the OEIS. Period 5 for mod 11 seems to be the only odd period > 1 (checked up to 1000 terms).
LINKS
Eric Weisstein's World of Mathematics, Pisano Number
Wikipedia, Pisano period
Index entries for linear recurrences with constant coefficients, signature (0, 3, 0, -1).
FORMULA
MAPLE
A292616 := gfun:-rectoproc({a(n) = 3 * a(n-2) - a(n-4), a(0) = 4, a(1) = 3, a(2) = 6, a(3) = 6}, a(n), remember): map(A292616, [$0..10^3]); # Muniru A Asiru, Oct 16 2017
MATHEMATICA
LinearRecurrence[{0, 3, 0, -1}, {4, 3, 6, 6}, 40]
(* Or, recomputing from Fibonacci numbers: *)
Join[{4, -1, 3}, Flatten[Table[{Fibonacci[2*n], Fibonacci[2*n+6]}, {n, 0, 18} ]]] // Accumulate
PROG
(GAP) a := [4, 3, 6, 6];; for n in [5..10^2] do a[n] := 3 * a[n-2] - a[n-4]; od; A292616 := a; # Muniru A Asiru, Oct 31 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Jean-François Alcover and Paul Curtz, Sep 20 2017
STATUS
approved