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

0,2

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

Formula

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

Prog

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

Crossrefs

Cf. A004016, A053416.

Sequence in context: A023224 A113743 A003215 * A133323 A002407 A098484

Adjacent sequences: A308682 A308683 A308684 * A308686 A308687 A308688

Keyword

nonn

Author

Peter Kagey, Jun 28 2019

Status

approved