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

0, 15, 84, 312, 852, 1878, 3654, 6546, 10680, 16668, 25002, 35910, 50136, 68190, 90462, 118200, 152274, 192828, 240480, 296880, 361962, 437832, 525756, 625440, 739146, 867864, 1011822, 1174062, 1354572, 1554114, 1775568, 2020848, 2289054, 2582760, 2905410

Offset: 1

Author

Martin Renner, Apr 17 2014

Keywords

• nonn

Comments

A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Hex Number.

Crossrefs

Cf. A018808, A241219, A003215.

Programs

PARI

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)))))}
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)}
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

Extensions

a(15)-a(16) from Martin Renner, Apr 27 2014

Terms a(17) and beyond from Andrew Howroyd, Sep 18 2017