OFFSET
1,2
COMMENTS
A sum-free sequence has no term that is the sum of a subset of its previous terms. There are an infinite number of sequences that are subsets of the squares and sum-free. This sequence is lexicographically the first.
LINKS
H. L. Abbott, On sum-free sequences
Eric W. Weisstein, MathWorld: A-Sequence
Wikipedia, Sum-free sequence
FORMULA
Conjecture: a(n) = 4*a(n-3) for n>9. G.f.: -x*(33*x^8 +112*x^7 +80*x^6 +28*x^5 +20*x^4 +12*x^3 +9*x^2 +4*x +1) / (4*x^3 -1). - Colin Barker, May 28 2013
EXAMPLE
a(10)=576 as 576 is the next square after a(9)=289 that cannot be formed from distinct sums of a(1),...,a(9) (1,4,9,16,36,64,144,256,289).
MATHEMATICA
memberQ[n1_, k1_] := If[Select[IntegerPartitions[n1^2, Length[k1], k1], Sort@#==Union@# &]=={}, False, True]; k={1}; n=1; While[Length[k]<20, (If[!memberQ[n, k], k=Append[k, n^2]]; n++)]; k
CROSSREFS
KEYWORD
nonn
AUTHOR
Frank M Jackson, May 25 2013
EXTENSIONS
More terms from Colin Barker, May 28 2013
a(33)-a(37) from Donovan Johnson, Dec 17 2013
STATUS
approved