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.

4, 32, 88, 116, 172, 200, 256, 284, 368, 424, 452, 508, 592, 620, 676, 704, 760, 788, 872, 956, 1012, 1040, 1096, 1180, 1208, 1264, 1292, 1348, 1376, 1432, 1544, 1600, 1628, 1684, 1796, 1852, 1880, 1936, 1964, 2020, 2048, 2132, 2188, 2216, 2272, 2356, 2440, 2468, 2552, 2608, 2636

Offset: 1

Author

Alexander M. Domashenko, Feb 10 2024

Keywords

• nonn
• easy

Comments

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.

Crossrefs

Cf. A004613.

Formula

a(n) = 7*A004613(n) - 3.