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A244880 Number of magic labelings of the cycle-of-loops graph LOOP X C_8 having magic sum n, where LOOP is the 1-vertex, 1-loop-edge graph.

%I A244880 #27 Mar 10 2025 05:42:45
%S A244880 1,47,650,4726,23219,87677,274132,743724,1806597,4016683,8306078,
%T A244880 16168802,29904823,52936313,90209192,148694104,238002057,371131047,
%U A244880 565361074,843316046,1234212155,1775313397,2513615996,3507784580,4830364045,6570292131,8835738822,11757299770,15491572031
%N A244880 Number of magic labelings of the cycle-of-loops graph LOOP X C_8 having magic sum n, where LOOP is the 1-vertex, 1-loop-edge graph.
%H A244880 Colin Barker, <a href="/A244880/b244880.txt">Table of n, a(n) for n = 0..1000</a>
%H A244880 R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]
%H A244880 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A244880 G.f.: (1+38*(x+x^5)+263*(x^2+x^4)+484*x^3+x^6) / (1-x)^9.
%F A244880 From _Colin Barker_, Jan 12 2017: (Start)
%F A244880 a(n) = (630 + 3051*n + 6570*n^2 + 8211*n^3 + 6503*n^4 + 3339*n^5 + 1085*n^6 + 204*n^7 + 17*n^8) / 630.
%F A244880 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.
%F A244880 (End)
%F A244880 (326*n^2-195*n+142)*a(n) +(-652*n^2-652*n-10725)*a(n-1) +(326*n^2+847*n+663)*a(n-2) +2*(-165*n^2-165*n-71)=0. - _R. J. Mathar_, Mar 10 2025
%p A244880 A244880:=n->(630 + 3051*n + 6570*n^2 + 8211*n^3 + 6503*n^4 + 3339*n^5 + 1085*n^6 + 204*n^7 + 17*n^8) / 630: seq(A244880(n), n=0..50); # _Wesley Ivan Hurt_, Sep 16 2017
%t A244880 CoefficientList[Series[(1 + 38 (x + x^5) + 263 (x^2 + x^4) + 484 x^3 + x^6)/(1 - x)^9, {x, 0, 28}], x] (* _Michael De Vlieger_, Sep 15 2017 *)
%o A244880 (PARI) Vec((1 + 6*x + x^2)*(1 + 32*x + 70*x^2 + 32*x^3 + x^4) / (1 - x)^9 + O(x^30)) \\ _Colin Barker_, Jan 12 2017
%Y A244880 Cf. A019298, A006325, A244497, A244879, A244873, A289992.
%K A244880 nonn,easy
%O A244880 0,2
%A A244880 _N. J. A. Sloane_, Jul 08 2014
%E A244880 Name corrected by _David J. Seal_, Sep 13 2017