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The number of triangular lattice points whose Euclidean distance from the origin is less than or equal to n.
2

%I #32 Apr 08 2022 04:03:28

%S 1,7,19,37,61,91,127,187,241,301,367,439,517,613,721,823,931,1045,

%T 1165,1303,1459,1615,1765,1921,2083,2263,2455,2653,2857,3055,3259,

%U 3481,3697,3949,4195,4447,4693,4957,5239,5527,5815,6109,6409,6715,7015,7333,7681

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

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

%H Peter Kagey, <a href="/A308685/b308685.txt">Table of n, a(n) for n = 0..1000</a>

%H Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/163704">Triangular Lattice Points close to the Origin</a>

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

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

%Y Cf. A004016, A053416.

%K nonn

%O 0,2

%A _Peter Kagey_, Jun 28 2019