A394394 - OEIS

%I #6 Mar 20 2026 00:02:16

%S 0,1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,

%T 231,253,276,300,325,349,376,404,433,463,492,524,557,591,626,662,699,

%U 737,776

%N Largest number of distinct lines determined by pairs of cell centers of a polycube with n cells.

%H Pontus von Brömssen, <a href="/A393939/a393939.gif">Illustration of the unique free polycube with 26 cells and no 3 collinear cells</a>.

%H <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.

%F a(n+1)-n <= a(n) <= n*(n-1)/2, with equality in the second part if and only if n <= 26 = largest k such that A393938(k,2) > 0. The first part is equivalent to n*(n-1)/2 - a(n) being nondecreasing.

%Y Cf. A038119, A393938, A393939 (number of optimal polycubes), A393992 (polyominoes), A393994 (distinct directions of lines).

%K nonn,more

%O 1,3

%A _Pontus von Brömssen_, Mar 19 2026