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 A173547 #12 Jun 29 2023 08:16:12
%S A173547 72,144,288,576,864,1440,2088,3024,3888,5904,6984,9432,12168,14904,
%T A173547 17928,23832,26784,33048,39672,46584,53640,65592,72504,85248,98928,
%U A173547 111816,125208,147528,160632,182808,206424,229176,252648,287928,310752
%N A173547 Number of 3 X 3 semimagic squares with distinct positive values and magic sum n.
%C A173547 In a semimagic squares the row and column sums must all be equal to the magic sum. a(n) is given by a quasipolynomial of degree 4 and period 840.
%C A173547 a(15) is the first term because the values 1,...,9 make magic sum 15. [From _Thomas Zaslavsky_, Mar 03 2010]
%D A173547 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 A173547 Thomas Zaslavsky, <a href="/A173547/b173547.txt">Table of n, a(n) for n=15..10000</a>.
%H A173547 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 A173547 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 A173547 <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 A173547 G.f.: 72 * 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)] }
%Y A173547 A173546 counts the same squares by upper bound on the entries. Cf. A108576, A108577, A108578, A108579, A173548, A173549.
%K A173547 nonn
%O A173547 15,1
%A A173547 _Thomas Zaslavsky_, Feb 21 2010, Feb 24 2010, Mar 03 2010