cp's OEIS Frontend

A241220 Number of lines through at least two points of a centered hexagonal grid of size n.

%I A241220 #13 Feb 16 2025 08:33:21
%S A241220 0,15,84,312,852,1878,3654,6546,10680,16668,25002,35910,50136,68190,
%T A241220 90462,118200,152274,192828,240480,296880,361962,437832,525756,625440,
%U A241220 739146,867864,1011822,1174062,1354572,1554114,1775568,2020848,2289054,2582760,2905410
%N A241220 Number of lines through at least two points of a centered hexagonal grid of size n.
%C A241220 A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.
%H A241220 Andrew Howroyd, <a href="/A241220/b241220.txt">Table of n, a(n) for n = 1..200</a>
%H A241220 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexNumber.html">Hex Number</a>.
%o A241220 (PARI)
%o A241220 c(n,s,fmin,fmax)={sum(k=1+s, n, max(0, fmax(k-s)-max(fmin(k)-1,if(k-2*s>0,fmax(k-2*s)))))}
%o A241220 b(n, u, v)={c(2*n-1, u, i->max(0,i-n)+1+i\u*v, i->min(i,n)+n-1+i\u*v)}
%o A241220 a(n)={3*((n>1)*(2*n-1) + sum(u=1, 2*n-3, sum(v=1, 2*n-2-u, if(gcd(u,v)==1, b(n,u,v), 0))))} \\ _Andrew Howroyd_, Sep 18 2017
%Y A241220 Cf. A018808, A241219, A003215.
%K A241220 nonn
%O A241220 1,2
%A A241220 _Martin Renner_, Apr 17 2014
%E A241220 a(15)-a(16) from _Martin Renner_, Apr 27 2014
%E A241220 Terms a(17) and beyond from _Andrew Howroyd_, Sep 18 2017