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A125198 Number of magical labelings of the octahedral graph of magic sum n.

%I A125198 #18 Apr 01 2018 11:30:53
%S A125198 1,8,40,144,417,1032,2272,4568,8545,15072,25320,40824,63553,95984,
%T A125198 141184,202896,285633,394776,536680,718784,949729,1239480,1599456,
%U A125198 2042664,2583841,3239600,4028584,4971624,6091905,7415136,8969728,10786976,12901249,15350184
%N A125198 Number of magical labelings of the octahedral graph of magic sum n.
%H A125198 Colin Barker, <a href="/A125198/b125198.txt">Table of n, a(n) for n = 0..1000</a>
%H A125198 M. M. Ahmed, <a href="http://arXiv.org/abs/math.CO/0405476">Algebraic Combinatorics of Magic Squares</a>, math.CO/0405476, p73.
%H A125198 R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]
%H A125198 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,14,0,-14,14,-6,1).
%F A125198 G.f.: (1+2*x+6*x^2+2*x^3+x^4)/((1-x)^7*(1+x)). [Stanley] - _N. J. A. Sloane_, Jul 07 2014
%F A125198 From _Colin Barker_, Jan 13 2017: (Start)
%F A125198 a(n) = (15*(31+(-1)^n) + 1152*n + 1216*n^2 + 720*n^3 + 250*n^4 + 48*n^5 + 4*n^6) / 480.
%F A125198 a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8) for n>7.
%F A125198 (End)
%p A125198 a := proc(r) local r2 ; r2 := r^6/120+r^5/10+25*r^4/48+3*r^3/2+38*r^2/15+12*r/5 ; if r mod 2 = 0 then r2+1 ; else r2+15/16 ; fi ; end: for n from 0 to 40 do printf("%d ",a(n)) ; od;
%t A125198 (1 + 2*x + 6*x^2 + 2*x^3 + x^4)/((1 - x)^7*(1 + x)) + O[x]^40 // CoefficientList[#, x]& (* _Jean-François Alcover_, Apr 01 2018 *)
%o A125198 (PARI) Vec((1+2*x+6*x^2+2*x^3+x^4)/((1-x)^7*(1+x)) + O(x^40)) \\ _Colin Barker_, Jan 13 2017
%K A125198 easy,nonn
%O A125198 0,2
%A A125198 _R. J. Mathar_, Jan 25 2007
%E A125198 Stanley reference added by _N. J. A. Sloane_, Jul 07 2014