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

1,1

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.

Links

Table of n, a(n) for n=1..51.

Formula

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

Crossrefs

Cf. A004613.

Sequence in context: A012036 A153794 A222326 * A108914 A052469 A211625

Adjacent sequences: A370079 A370080 A370081 * A370083 A370084 A370085

Keyword

nonn,easy

Author

Alexander M. Domashenko, Feb 10 2024

Status

approved