

A226076


Lexicographically least sequence of squares that are sumfree.


1



1, 4, 9, 16, 36, 64, 144, 256, 289, 576, 1024, 1156, 2304, 4096, 4624, 9216, 16384, 18496, 36864, 65536, 73984, 147456, 262144, 295936, 589824, 1048576, 1183744, 2359296, 4194304, 4734976, 9437184, 16777216, 18939904, 37748736, 67108864, 75759616, 150994944
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OFFSET

1,2


COMMENTS

A sumfree 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 sumfree. This sequence is lexicographically the first.


LINKS

Table of n, a(n) for n=1..37.
H. L. Abbott, On sumfree sequences
Eric W. Weisstein, MathWorld: ASequence
Wikipedia, Sumfree sequence


FORMULA

Conjecture: a(n) = 4*a(n3) 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

Cf. A225947.
Sequence in context: A106575 A025620 A117218 * A272711 A018228 A204503
Adjacent sequences: A226073 A226074 A226075 * A226077 A226078 A226079


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



