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A123337
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Number of ordered ways to write n as the sum of 5 squares less than 5.
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2
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1, 5, 10, 10, 10, 21, 30, 20, 15, 35, 50, 40, 20, 25, 60, 60, 30, 20, 40, 30, 45, 70, 60, 80, 60, 50, 90, 70, 60, 30, 120, 80, 30, 90, 120, 20, 35, 60, 30, 120, 35, 60, 60, 50, 20, 61, 60, 10, 10, 50, 40, 30, 25, 20, 30, 0, 10, 20, 20, 10, 0, 20, 0, 0, 5, 5, 10, 0, 5, 0, 0, 0, 0, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Through n = 24, a(n) = number of ordered ways to write n as the sum of 5 squares. For n > 24, we must exclude sums which include 5^2, 6^2 and the like. The values of n such that a(n) = 0 are 55, 60, 62, 63, 67, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79 and all n > 80. Without the restriction on the size of squares, all natural numbers can be written as the sum of 4 squares, as Lagrange proved in 1750.
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EXAMPLE
| a(0) = 1 because the unique such sum is 0 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2.
a(1) = 5 because there are 5 permutations of 1 = 1^2 + 0^2 + 0^2 + 0^2 + 0^2, such as 1 = 0^2 + 1^2 + 0^2 + 0^2 + 0^2.
a(2) = 10 because there are 10 permutations of 2 = 1^2 + 1^2 + 0^2 + 0^2 + 0^2, such as 2 = 1^2 + 0^2 + 1^2 + 0^2 + 0^2.
a(5) = 21 because of the unique sum 5 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 and also 20 permutations of 5 = 2^2 + 1^2 + 0^2 + 0^2 + 0^2.
a(16) = 30 because there are 5 permutations of 16 = 4^2 + 0^2 + 0^2 + 0^2 + 0^2 and 5 permutations of 16 = 0^2 + 2^2 + 2^2 + 2^2 + 2^2 and 20 permutations of 16 = 3^2 + 2^2 + 1^2 + 1^2 + 1^2.
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CROSSREFS
| Cf. A000118, A014110.
Sequence in context: A135912 A200990 A040020 * A038671 A101866 A201033
Adjacent sequences: A123334 A123335 A123336 * A123338 A123339 A123340
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KEYWORD
| easy,fini,full,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 11 2006
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