%I #16 Apr 07 2020 10:42:17
%S 1,15,130,760,3355,12043,36935,100135,245870,556580,1177295,2351165,
%T 4469610,8141210,14284170,24247962,39970575,64178685,100639000,
%U 154470030,232524589,343854445,500269705,717006745,1013519780,1414412506,1950527645,2660213675,3590789540,4800229700
%N Number of 6 X 6 traceless symmetric magic squares with magic sum n.
%H Colin Barker, <a href="/A244878/b244878.txt">Table of n, a(n) for n = 0..1000</a>
%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (9,-35,75,-90,42,42,-90,75,-35,9,-1).
%F G.f.: (1 + 6*x + 30*x^2 + 40*x^3 + 30*x^4 + 6*x^5 + x^6) / ((1 - x)^10*(1 + x)).
%F a(n) = (945*(507+5*(-1)^n) + 1480896*n + 2062800*n^2 + 1747040*n^3 + 989100*n^4 + 383628*n^5 + 100800*n^6 + 17160*n^7 + 1710*n^8 + 76*n^9) / 483840. - _Colin Barker_, Jan 12 2017
%o (PARI) Vec((1 + 6*x + 30*x^2 + 40*x^3 + 30*x^4 + 6*x^5 + x^6) / ((1 - x)^10*(1 + x)) + O(x^30)) \\ _Colin Barker_, Jan 12 2017
%Y Row n=6 of A333351.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jul 08 2014
|