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 A173726 #10 Jun 29 2023 09:22:39 %S A173726 1,2,4,7,10,16,21,30,34,53,55,77,87,110,118,162,165,210,220,275,286, %T A173726 360,360,439,463,546,555,675,678,800,818,952,970,1132,1133,1311,1341, %U A173726 1519,1530,1764,1772,2002,2028,2275,2299,2592,2590,2900,2939,3250,3265,3644 %N A173726 Number of reduced, normalized 3x3 semimagic squares with magic sum n. %C A173726 In a semimagic square the row and column sums must all equal the magic sum. The symmetries are permutation of rows and columns and reflection in a diagonal. A "reduced" square has least entry 0. There is one normalized square for each symmetry class of reduced squares. See A173725 for a general normal form. a(n) is given by a quasipolynomial of degree 4 and period 840. %D A173726 Matthias Beck and Thomas Zaslavsky, An enumerative geometry for magic and magilatin labellings, Annals of Combinatorics, 10 (2006), no. 4, pages 395-413. MR 2007m:05010. Zbl 1116.05071. %H A173726 Thomas Zaslavsky, <a href="/A173726/b173726.txt">Table of n, a(n) for n=12..10000</a>. %H A173726 Matthias Beck, Thomas Zaslavsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Zaslavsky/sls.html">Six Little Squares and How Their Numbers Grow </a>, J. Int. Seq. 13 (2010), 10.6.2. %H A173726 Matthias Beck and Thomas Zaslavsky, <a href="https://people.math.binghamton.edu/zaslav/Tpapers/SLSfiles/">"Six Little Squares and How their Numbers Grow" Web Site</a>: Maple worksheets and supporting documentation. %H A173726 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (-2, -3, -3, -2, 0, 3, 6, 9, 10, 9, 5, 0, -6, -11, -14, -14, -11, -6, 0, 5, 9, 10, 9, 6, 3, 0, -2, -3, -3, -2, -1). %e A173726 a(12) is the first term because the values 0,...,8 make magic sum 12. a(12)=1 because there is only one normal form with values 0 to 8: (by rows) 0,4,8;5,6,1;7,2,3. a(13)=2 because the values 0,...,5,7,8,9 give two normal forms: 0,4,9;5,7,1;8,2,3 and 0,4,9;5,7,1;8,2,3. %Y A173726 Cf. A173547, A173725. A173724 counts squares by largest cell value. %K A173726 nonn %O A173726 12,2 %A A173726 _Thomas Zaslavsky_, Feb 23 2010