This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365963 #15 Dec 07 2023 14:53:34
%S A365963 0,1,4,6,14,8,11,12,20,20,32,28,38,30,32,26,26,24,30,20,50,40,49,69,
%T A365963 61,33,49,37,46,41,52,41,53,42,61,53,52,61,34,41,50,57,85,70,73,65,69,
%U A365963 65,60,53,56,69,49,44,45,105,82,58,64,88,86,76,74,94,86,82
%N A365963 Let I(n) be the moment of inertia of the polyomino with binary code A246521(n+1) about an axis through its center of mass perpendicular to the plane of the polyomino, the polyomino having a unit point mass in the center of each of its cells. a(n) is I(n) times the number of cells of the polyomino.
%C A365963 If the cells have a uniform density of 1 instead of point masses in the centers, the moment of inertia is I(n) + k/6 = a(n)/k + k/6, where k is the number of cells.
%H A365963 Pontus von Brömssen, <a href="/A365963/b365963.txt">Table of n, a(n) for n = 1..6473</a> (rows 1..10).
%H A365963 <a href="/index/Mo#moment_of_inertia">Index entries for sequences related to moment of inertia</a>.
%H A365963 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.
%F A365963 If the centers of the cells of the polyomino have coordinates (x_i,y_i), 1 <= i <= k, its moment of inertia is Sum_{i=1..k} x_i^2+y_i^2 - (Sum_{i=1..k} x_i)^2/k - (Sum_{i=1..k} y_i)^2/k.
%e A365963 As an irregular triangle:
%e A365963 0;
%e A365963 1;
%e A365963 4, 6;
%e A365963 14, 8, 11, 12, 20;
%e A365963 20, 32, 28, 38, 30, 32, 26, 26, 24, 30, 20, 50;
%e A365963 ...
%e A365963 The five tetrominoes have moments of inertia 7/2, 2, 11/4, 3, 5 (in the order they appear in A246521). Multiplying these numbers by 4, we obtain the 4th row.
%e A365963 The last term of the k-th row of the irregular triangle corresponds to the straight k-omino, whose moment of inertia is k*(k^2-1)/12, so the last term of the k-th row is k^2*(k^2-1)/12 = A002415(k). (This ought to be the largest term of the k-th row.)
%Y A365963 Cf. A000105 (row lengths), A002415, A246521, A365964 (row minima).
%K A365963 nonn,tabf
%O A365963 1,3
%A A365963 _Pontus von Brömssen_, Sep 23 2023