%I #4 Jun 27 2024 22:26:30
%S 1,18,93,296,725,1506,2793,4768,7641,11650,17061,24168,33293,44786,
%T 59025,76416,97393,122418,151981,186600,226821,273218,326393,386976,
%U 455625,533026,619893,716968,825021,944850,1077281,1223168,1383393,1558866,1750525,1959336
%N Vertical moments of inertia of a unit lozenge tiling of the hexagon with side lengths n (see references for exact configuration).
%D J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 6, note a(2) is erroneous in this reference, cf. A071092).
%H Ilse Fischer, <a href="https://arxiv.org/abs/math/0012126">Moments of inertia associated with the lozenge tilings of a hexagon</a>, 2000.
%H J. Propp, <a href="http://faculty.uml.edu/jpropp/update.pdf">Updated article</a>
%H J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), <a href="http://www.msri.org/publications/books/Book38/contents.html">New Perspectives in Algebraic Combinatorics</a>
%H <a href="/index/Mo#moment_of_inertia">Index entries for sequences related to moment of inertia</a>.
%F a(n) = (7*n^4 - n^2) / 6.
%K nonn
%O 1,2
%A _Sean A. Irvine_, Jun 27 2024