A308685 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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) */