This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370082 #36 Mar 24 2024 12:50:19 %S A370082 4,32,88,116,172,200,256,284,368,424,452,508,592,620,676,704,760,788, %T A370082 872,956,1012,1040,1096,1180,1208,1264,1292,1348,1376,1432,1544,1600, %U A370082 1628,1684,1796,1852,1880,1936,1964,2020,2048,2132,2188,2216,2272,2356,2440,2468,2552,2608,2636 %N A370082 The number of square lattice nodes inside the n-th largest octagon with angles 3*Pi/4, along the perimeter of which there are only 8 lattice nodes - at the vertices of the octagon. %C A370082 The adjacent sides of an octagon are not equal, the ratio of the larger side to the smaller one is sqrt(2), its area is 7 times the square of the shorter side. Using Pick's formula N = S - V/2 + 1 we obtain N = S - 3 = 7*A004613(n) - 3. %F A370082 a(n) = 7*A004613(n) - 3. %Y A370082 Cf. A004613. %K A370082 nonn,easy %O A370082 1,1 %A A370082 _Alexander M. Domashenko_, Feb 10 2024