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A053416
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Circle numbers (version 4): a(n)= number of points (i+j/2,j*sqrt(3)/2), i,j integers (triangular grid) contained in a circle of diameter n, centered at (0,0).
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11
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1, 1, 7, 7, 19, 19, 37, 43, 61, 73, 91, 109, 127, 151, 187, 199, 241, 253, 301, 313, 367, 397, 439, 475, 517, 571, 613, 661, 721, 757, 823, 859, 931, 979, 1045, 1111, 1165, 1237, 1303, 1381, 1459, 1519, 1615, 1663, 1765, 1813, 1921, 1993, 2083, 2173, 2263
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OFFSET
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0,3
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COMMENTS
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In other words, number of points in a hexagonal lattice covered by a circle of diameter n if the center of the circle is chosen at a grid point. - Hugo Pfoertner, Jan 07 2007
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LINKS
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H. v. Eitzen, Table of n, a(n) for n=0..1000
Index entries for sequences related to A2 = hexagonal = triangular lattice
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FORMULA
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a(n)/(n/2)^2->Pi*2/sqrt(3)
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MATHEMATICA
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a[n_] := (m = Ceiling[n/2] + 3; Sum[Boole[ 4*(i^2 + i*j + j^2) <= n^2], {i, -m, m}, {j, -m, m}] ); Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jun 06 2013 *)
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CROSSREFS
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Cf. A003215, A125849, A125850, A125851, A125852.
Cf. A053411, A053414, A053415, A053417.
Sequence in context: A070919 A070847 A195863 * A213031 A094248 A146804
Adjacent sequences: A053413 A053414 A053415 * A053417 A053418 A053419
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KEYWORD
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easy,nonn,changed
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 10 2000
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EXTENSIONS
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Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar
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STATUS
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approved
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