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A121343
a(n) = Fibonacci(n) mod n(n+1)/2.
4
0, 0, 1, 2, 3, 5, 8, 13, 21, 34, 0, 23, 66, 51, 62, 10, 35, 67, 19, 1, 45, 89, 1, 229, 168, 275, 298, 236, 319, 59, 155, 125, 309, 376, 407, 485, 630, 628, 419, 466, 615, 370, 517, 343, 663, 830, 988, 1033, 168, 624, 700, 746, 1167, 158, 872, 1105, 609, 610, 59, 1181, 0, 1, 125
OFFSET
0,4
LINKS
FORMULA
A000045(n) modulo A000217(n).
EXAMPLE
a(11)=23 since Fib(11)=89==23(mod (11*12/2)).
MAPLE
a:= proc(n) local r, M, p, m; r, M, p, m:=
<<1|0>, <0|1>>, <<0|1>, <1|1>>, n, n*(n+1)/2;
do if irem(p, 2, 'p')=1 then r:= r.M mod m fi;
if p=0 then break fi; M:= M.M mod m
od; r[1, 2]
end:
seq(a(n), n=0..100); # Alois P. Heinz, Nov 26 2016
MATHEMATICA
f[n_] := If[n == 0, 0, Mod[Fibonacci@n, n(n + 1)/2]]; f /@ Range[0, 62] (* Robert G. Wilson v, Aug 31 2006 *)
Join[{0}, Mod[First[#], Last[#]]&/@With[{nn=70}, Thread[{Fibonacci[ Range[ nn]], Accumulate[Range[nn]]}]]] (* Harvey P. Dale, May 21 2012 *)
PROG
(PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
a(n)=lift(fibmod(n, n*(n+1)/2)) \\ Charles R Greathouse IV, Jun 20 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 29 2006
EXTENSIONS
Edited by N. J. A. Sloane, Jul 01 2008 at the suggestion of R. J. Mathar
STATUS
approved