A308685 The number of triangular lattice points whose Euclidean distance from the origin is less than or equal to n.

1, 7, 19, 37, 61, 91, 127, 187, 241, 301, 367, 439, 517, 613, 721, 823, 931, 1045, 1165, 1303, 1459, 1615, 1765, 1921, 2083, 2263, 2455, 2653, 2857, 3055, 3259, 3481, 3697, 3949, 4195, 4447, 4693, 4957, 5239, 5527, 5815, 6109, 6409, 6715, 7015, 7333, 7681

Offset: 0

Author

Peter Kagey, Jun 28 2019

Keywords

• nonn

Comments

Also the sum of the first n^2+1 terms of A004016.

Links

• Peter Kagey, Table of n, a(n) for n = 0..1000
• Code Golf Stack Exchange, Triangular Lattice Points close to the Origin

Crossrefs

Cf. A004016, A053416.

Programs

PARI

a(n)=1+2*vecsum(Vec(qfrep([2,1;1,2],n^2,1))) /* Georg Fischer, Apr 07 2022 (from codegolf link) */

Formula

a(n) = A053416(2*n).