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A125196 Number of magic labelings of the Petersen graph with magic sum n.

%I A125196 #17 Sep 10 2024 12:47:48
%S A125196 1,6,27,87,228,513,1034,1914,3315,5440,8541,12921,18942,27027,37668,
%T A125196 51428,68949,90954,118255,151755,192456,241461,299982,369342,450983,
%U A125196 546468,657489,785869,933570,1102695,1295496
%N A125196 Number of magic labelings of the Petersen graph with magic sum n.
%H A125196 Vincenzo Librandi, <a href="/A125196/b125196.txt">Table of n, a(n) for n = 0..1000</a>
%H A125196 R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]
%H A125196 M. M. Ahmed, <a href="http://arXiv.org/abs/math.CO/0405476">Algebraic Combinatorics of Magic Squares</a>, math.CO/0405476.
%H A125196 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,5,5,-9,5,-1).
%F A125196 a(n) = (1/32)*(29*C(n+5,5) + 21*C(n+4,5) + 126*C(n+3,5) - 34*C(n+2,5) + 21*C(n+1,5) - 3*C(n,5) + 3*(-1)^n). [Stanley]. - _N. J. A. Sloane_, Jul 07 2014
%F A125196 G.f.: (x^4+x^3+6x^2+x+1)/((1-x)^6*(1+x)) [Stanley; Ahmed].
%p A125196 a := proc(r) local r1 ; r1 := r^5/24+5*r^4/16+25*r^3/24+15*r^2/8+23*r/12 ; if r mod 2 = 0 then r1+1 ; else r1+13/16 ; fi ; end: for n from 0 to 30 do printf("%d ",a(n)) ; od;
%t A125196 CoefficientList[Series[(x^4 + x^3 + 6x^2 + x + 1)/(1 - x)^6/(1 + x), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 12 2012 *)
%t A125196 LinearRecurrence[{5,-9,5,5,-9,5,-1},{1,6,27,87,228,513,1034},40] (* _Harvey P. Dale_, Sep 10 2024 *)
%K A125196 easy,nonn
%O A125196 0,2
%A A125196 _R. J. Mathar_, Jan 25 2007
%E A125196 Stanley reference added by _N. J. A. Sloane_, Jul 07 2014