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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.
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%I #36 Mar 24 2024 12:50:19

%S 4,32,88,116,172,200,256,284,368,424,452,508,592,620,676,704,760,788,

%T 872,956,1012,1040,1096,1180,1208,1264,1292,1348,1376,1432,1544,1600,

%U 1628,1684,1796,1852,1880,1936,1964,2020,2048,2132,2188,2216,2272,2356,2440,2468,2552,2608,2636

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

%Y Cf. A004613.

%K nonn,easy

%O 1,1

%A _Alexander M. Domashenko_, Feb 10 2024