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A025416
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Least sum of 4 nonzero squares in exactly n ways.
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7
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0, 4, 31, 28, 52, 82, 90, 135, 130, 162, 198, 202, 252, 234, 210, 346, 306, 322, 423, 370, 330, 418, 390, 462, 378, 490, 598, 450, 546, 618, 522, 594, 642, 682, 570, 770, 714, 690, 762, 906, 738, 630, 1030, 850, 1035, 978, 858, 954, 810, 1197, 1146, 882, 1090, 1206
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OFFSET
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0,2
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COMMENTS
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Conjecture: The sequence never becomes monotonic increasing. - Jon Perry, Nov 03 2012
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 31 because 31 = 1 + 1 + 4 + 25 = 4 + 9 + 9 + 9 and no others.
a(3) = 28 because 28 = 1 + 1 + 1 + 25 = 1 + 9 + 9 + 9 = 4 + 4 + 4 + 16 and no others.
a(4) = 52 because 52 = 1 + 1 + 1 + 49 = 1 + 1 + 25 + 25 = 4 + 16 + 16 + 16 = 9 + 9 + 9 + 25 and no others.
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MATHEMATICA
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nn = 40; t = Select[Flatten[Table[a^2 + b^2 + c^2 + d^2, {a, nn}, {b, a}, {c, b}, {d, c}]], # <= nn^2 + 3 &]; {t1, t2} = Transpose[Sort[Tally[t]]]; u = Union[t2]; c = Complement[Range[u[[-1]]], u]; If[c == {}, last = u[[-1]], last = c[[1]] - 1]; Join[{0}, Table[t1[[Position[t2, n, 1, 1][[1, 1]]]], {n, last}]] (* T. D. Noe, Nov 02 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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