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

1,2

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.

Prog

(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

Crossrefs

Cf. A018808, A241219, A003215.

Sequence in context: A247958 A108674 A050405 * A279740 A281189 A206383

Adjacent sequences: A241217 A241218 A241219 * A241221 A241222 A241223

Keyword

nonn

Author

Martin Renner, Apr 17 2014

Extensions

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

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

Status

approved