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 A381976 #22 Sep 04 2025 16:17:04 %S A381976 1,0,0,0,0,0,0,2332,216285 %N A381976 a(n) is the number of distinct solutions to the Partridge Puzzle of size n. %C A381976 a(n) is the number of packings of squares of side 1..n to fill the square of side n(n+1)/2 under the condition that there are: 1 square of size 1 X 1, 2 squares of size 2 X 2, 3 squares of size 3 X 3, ..., n squares of size n X n. %C A381976 The sequence comes from the formula 1^3 + 2^3 + ... + n^3 = (1+2+...+n)^2 = (n(n+1)/2)^2 (Nicomachus's theorem), so that the areas of the squares sum up to the area of the big square. %C A381976 Rotations and mirrorings of the packings are not counted as distinct (there are in total 8 distinct variations of each packing). %C A381976 Interestingly, for n = 9 the area of the big square is equal to 45*45 = 2025 making this problem a problem of the year 2025. %H A381976 Matt Parker, <a href="https://www.youtube.com/watch?v=eqyuQZHfNPQ">The impossible puzzle with over a million solutions!</a>, YouTube video. %H A381976 Danila Potapov, <a href="https://habr.com/ru/articles/889410/">How I solved a problem of the year 2025</a> (in Russian). %H A381976 Robert T. Wainwright, <a href="https://mathpuzzle.com/partridge.html">The Partridge Puzzle</a>. %Y A381976 Cf. A369891. %K A381976 nonn,more,changed %O A381976 1,8 %A A381976 _Danila Potapov_, Mar 11 2025