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Search: id:A077770
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| A077770 |
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Number of ordered pairs of integers (x,y) with n^2 < x^2 + y^2 < (n+1)^2; number of lattice points between circles of radii n and n+1. |
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+0
3
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| 0, 4, 12, 16, 20, 28, 32, 44, 52, 52, 56, 60, 76, 80, 84, 84, 92, 104, 116, 116, 112, 140, 132, 136, 148, 148, 164, 160, 164, 180, 176, 204, 196, 204, 216, 196, 228, 216, 252, 236, 224, 260, 260, 284, 272, 260, 292, 288, 308, 300, 316, 312, 300, 332, 320, 364
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Note that 2*A077768(n)-a(n)/4 is the characteristic sequence for the Beatty sequence A001951(n).
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LINKS
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Eric Weisstein's World of Mathematics, Gauss's Circle Problem
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FORMULA
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a(n) = A051132(n+1) - A000328(n)
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MATHEMATICA
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Needs["NumberTheory`NumberTheoryFunctions`"]; Table[Sum[SumOfSquaresR[2, k], {k, n^2 + 1, (n + 1)^2 - 1}], {n, 0, 100}]
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CROSSREFS
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Cf. A000328, A001951, A051132, A077768.
Sequence in context: A145199 A082420 A053362 this_sequence A108269 A081523 A053006
Adjacent sequences: A077767 A077768 A077769 this_sequence A077771 A077772 A077773
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 20 2002
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