A053458 Open disk numbers (version 3): a(n)= number of points (i+j/2,j*sqrt(3)/2), i,j integers (triangular grid) contained in a open disk of diameter n, centered at (0,0).

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