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 A053416 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). 15
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 Same as above but "number of disks (r = 1)" instead of "number of points". See illustration in links. - Kival Ngaokrajang, Apr 06 2014 LINKS H. v. Eitzen, Table of n, a(n) for n = 0..1000 Kival Ngaokrajang, Illustration of initial terms Index entries for sequences related to A2 = hexagonal = triangular lattice FORMULA a(n)/(n/2)^2->Pi*2/sqrt(3). a(n) >= A053458(n). - R. J. Mathar, Nov 22 2022 a(2*n) = A308685(n). - R. J. Mathar, Nov 22 2022 MAPLE A053416 := proc(d) local a, j, imin, imax ; a := 0 ; for j from -floor(d/sqrt(3)) do if j^2*3 > d^2 and j> 0 then break ; end if; imin := ceil((-j-sqrt(d^2-3*j^2))/2) ; imax := floor((-j+sqrt(d^2-3*j^2))/2) ; a := a+imax-imin+1 ; end do: a ; end proc: seq(A053416(d), d=0..30) ; # R. J. Mathar, Nov 22 2022 MATHEMATICA a[n_] := Sum[Boole[4*(i^2 + i*j + j^2) <= n^2], {i, -n, n}, {j, -n, n}]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 06 2013, updated Apr 08 2022 to correct a discrepancy wrt b-file noticed by Georg Fischer *) CROSSREFS Cf. A003215, A125849, A125850, A125851, A125852. Cf. A053411, A053414, A053415, A053417, A053458 (open disk), A308685 (bisection). Sequence in context: A070919 A070847 A195863 * A213031 A299453 A300091 Adjacent sequences: A053413 A053414 A053415 * A053417 A053418 A053419 KEYWORD easy,nonn AUTHOR Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 10 2000 EXTENSIONS Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified December 2 07:04 EST 2023. Contains 367510 sequences. (Running on oeis4.)