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 A173725 #17 Jun 29 2023 09:21:02
%S A173725 1,2,4,8,12,20,29,42,54,82,97,131,169,207,249,331,372,459,551,647,745,
%T A173725 911,1007,1184,1374,1553,1739,2049,2231,2539,2867,3183,3509,3999,4316,
%U A173725 4820,5340,5835,6350,7104,7607,8352,9132,9882,10651,11724,12472,13551
%N A173725 Number of symmetry classes of 3 X 3 semimagic squares with distinct positive values and magic sum n.
%C A173725 In a semimagic square the row and column sums must all be equal to the magic sum. The symmetries are permutation of rows and columns and reflection in a diagonal. a(n) is given by a quasipolynomial of degree 4 and period 840.
%D A173725 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 A173725 Thomas Zaslavsky, <a href="/A173725/b173725.txt">Table of n, a(n) for n = 15..10000</a>.
%H A173725 Matthias Beck and 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 A173725 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 A173725 <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (-2, -3, -2, 0, 3, 6, 8, 9, 7, 3, -4, -10, -15, -16, -14, -8, 0, 8, 14, 16, 15, 10, 4, -3, -7, -9, -8, -6, -3, 0, 2, 3, 2, 1).
%F A173725 G.f.: (x^3)/(1-x^3) * { x^7/[(x-1)*(x^2-1)^3] + 2x^7/[(x-1)*(x^2-1)*(x^4-1)] + x^7/[(x-1)*(x^6-1)] + x^7/[(x^2-1)^2*(x^3-1)] + x^7/[(x^2-1)*(x^5-1)] + x^7/[(x^3-1)*(x^4-1)] + x^7/(x^7-1) + x^9/[(x-1)*(x^4-1)^2] + 2*x^9/[(x^2-1)*(x^3-1)*(x^4-1)] + 2*x^9/[(x^3-1)*(x^6-1)] + x^9/[(x^4-1)*(x^5-1)] + x^11/[(x^3-1)*(x^4-1)^2] + x^11/[(x^3-1)*(x^8-1)] + x^11/[(x^5-1)*(x^6-1)] + x^13/[(x^5-1)*(x^8-1)] }. - _Thomas Zaslavsky_, Mar 03 2010
%e A173725 a(15) is the first term because the values 1,...,9 make magic sum 15. By symmetries one can assume a_{11} is smallest, and a_{11} < a_{12} < a_{21} < a_{31} < a_{13}. a(15)=1 because there is only one normal form with values 1,...,9 (equivalent to the classical 3 X 3 magic square). a(16)=2 because the values 1,...,8,10 give two normal forms.
%Y A173725 Cf. A173547, A173726. A173723 counts symmetry types by largest cell value.
%K A173725 nonn
%O A173725 15,2
%A A173725 _Thomas Zaslavsky_, Feb 23 2010