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A223726 Multiplicities for A004433: sum of four distinct nonzero squares. 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 1, 1, 1, 3, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 5, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 4, 2, 1, 2, 3, 1, 5, 2, 2, 2, 2, 3, 4, 3, 1, 4, 1, 1, 4, 2, 2, 2, 5, 3, 1, 6, 3, 3, 1, 2, 1, 1, 4, 4, 1, 2, 5, 1, 3, 7, 3, 2, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,16
COMMENTS
The number A004433(n) can be partitioned into four distinct parts, each of which is a nonzero square, and a(n) gives the multiplicity which is the number of different partitions of this type.
LINKS
FORMULA
a(n) = k if there are k different quadruples [s(1),s(2),2(3),s(4)] with increasing positive entries with sum(s(j)^2,j=1..4) = A004433(n), n >= 1.
EXAMPLE
a(1) = 1 because A004433(1) = 30 has only one representation as sum of four distinct nonzero squares, given by the quadruple [1,2,3,4]: 1^2 + 2^2 + 3^2 + 4^2 = 30.
a(16) = 3 because for A004433(3) = 78 the three different quadruples are [1, 2, 3, 8], [1, 4, 5, 6] and [2, 3, 4, 7].
a(48) = 5 because A004433(48) = 126 has five different representations given by the five quadruples [1, 3, 4, 10], [1, 5, 6, 8], [2, 3, 7, 8], [2, 4, 5, 9], [4, 5, 6, 7].
CROSSREFS
Sequence in context: A030395 A031243 A030394 * A223728 A030596 A031277
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Mar 26 2013
STATUS
approved

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Last modified April 20 11:59 EDT 2024. Contains 371838 sequences. (Running on oeis4.)