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 A053458 Open disk numbers (version 3): a(n) is the number of points (i+j/2,j*sqrt(3)/2), i,j integers (triangular grid) contained in an open disk of diameter n, centered at (0,0). 6
 0, 1, 1, 7, 13, 19, 31, 43, 55, 73, 85, 109, 121, 151, 169, 199, 235, 253, 295, 313, 361, 397, 433, 475, 511, 571, 595, 661, 703, 757, 817, 859, 925, 979, 1039, 1111, 1159, 1237, 1285, 1381, 1453, 1519, 1597, 1663, 1759, 1813, 1915, 1993, 2077, 2173, 2257 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n)/(n/2)^2 --> Pi*2/sqrt(3). LINKS Table of n, a(n) for n=0..50. MAPLE A053458 := 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 := (-j-sqrt(d^2-3*j^2))/2 ; if type(imin, integer) then imin := imin+1 ; else imin := ceil(imin) ; end if; imax := (-j+sqrt(d^2-3*j^2))/2 ; if type(imax, integer) then imax := imax -1 ; else imax := floor(imax) ; end if; a := a+imax-imin+1 ; end do: a ; end proc: seq(A053458(d), d=0..30) ; # R. J. Mathar, Nov 22 2022 CROSSREFS Cf. A053416 (closed disk), A053456, A053457, A053459. Sequence in context: A091180 A272381 A242190 * A040058 A172057 A173176 Adjacent sequences: A053455 A053456 A053457 * A053459 A053460 A053461 KEYWORD easy,nonn AUTHOR Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 13 2000 STATUS approved

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Last modified June 7 04:44 EDT 2023. Contains 363151 sequences. (Running on oeis4.)