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%I #26 Apr 04 2024 10:08:45
%S 0,1,4,8,20,33,52,78,108,156,212,264,340,425,528,640
%N a(n) is n times the minimum moment of inertia of an n-celled polyomino about an axis through the center of mass perpendicular to the plane of the polyomino, with a unit point mass in the center of each of the cells.
%H Pontus von Brömssen, <a href="/A365964/a365964.svg">Illustration of the optimal polyominoes for 1 <= n <= 13, with their centers of mass marked with a dot</a>.
%H Pontus von Brömssen, <a href="https://oeis.org/plot2a?name1=A365964&name2=A000578&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawpoints=true">Plot of a(n)/n^3 vs n</a>, using Plot2.
%H <a href="/index/Mo#moment_of_inertia">Index entries for sequences related to moment of inertia</a>.
%H <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.
%F a(n) ~ n^3/(2*Pi).
%e For some n, there are more than one polyomino that have the minimum possible moment of inertia. For n = 5, for example, both the P-pentomino and the X-pentomino have the minimum possible moment of inertia a(5)/5 = 4; and for n = 11, the two undecominoes below both have the minimum possible moment of inertia a(11)/11 = 212/11.
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%e Also for n = 16 there are two polyominoes with the minimum moment of inertia a(16)/16 = 40: the 4 X 4 square and the 5 X 4 square with the corner cells removed. - _Pontus von Brömssen_, Apr 03 2024
%Y Row minima of A365963.
%Y Cf. A000578.
%K nonn,more
%O 1,3
%A _Pontus von Brömssen_, Sep 23 2023
%E a(14)-a(16) from _Pontus von Brömssen_, Apr 03 2024
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