OFFSET
1,1
COMMENTS
This sequence is a solution, along with three other sequences, of a system of four complementary equations; see A297464. It is the "anti-tribonacci" sequence, in analogy with the anti-Fibonacci sequence, A075326. - Clark Kimberling, Apr 22 2018
LINKS
Peter Kagey, Table of n, a(n) for n = 1..10000
William Lowell Putnam Competition, Problem B2, 2015.
MAPLE
S:= {$1..1000}: A:= NULL:
while nops(S) >= 3 do
T:= S[1..3];
s:= convert(T, `+`);
S:= S[4..-1] minus {s};
A:= A, s
od:
A; # Robert Israel, Dec 22 2015
MATHEMATICA
f[n_] := Block[{a = {}, r = Range@ n, s}, Do[If[Length@ r > 4, s = Total@ Take[r, 3 ]; AppendTo[a, s]; r = Drop[#, 3] &@ DeleteCases[r, x_ /; x == s], Break[]], {k, n}]; a]; f@ 184 (* Michael De Vlieger, Dec 22 2015 *)
morph = Nest[Flatten[# /. {0 -> {1, 2, 0}, 1 -> {1, 1, 0}, 2 -> {1, 0, 0}}] &, {0}, 9]; A265389 = Accumulate[Prepend[Drop[Flatten[morph /. Thread[{0, 1, 2} -> {{1, 1, 4}, {1, 2, 3}, {1, 3, 2}}]], 1] + 8, 6]];
Take[A265389, 100] (* Peter J. C. Moses, May 03 2018 *)
PROG
(Ruby)
x = (1..10000).to_a
(0...1000).collect do
y = x.shift(3).reduce(:+); x.delete_at x.index(y); y
end
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Dec 08 2015
STATUS
approved