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A245827 Szeged index of the grid graph P_3 X P_n.

%I A245827 #22 Sep 08 2022 08:46:09
%S A245827 4,59,216,526,1040,1809,2884,4316,6156,8455,11264,14634,18616,23261,
%T A245827 28620,34744,41684,49491,58216,67910,78624,90409,103316,117396,132700,
%U A245827 149279,167184,186466,207176,229365,253084,278384,305316,333931,364280,396414,430384,466241,504036,543820
%N A245827 Szeged index of the grid graph P_3 X P_n.
%H A245827 Vincenzo Librandi, <a href="/A245827/b245827.txt">Table of n, a(n) for n = 1..1000</a>
%H A245827 S. Klavzar, A. Rajapakse, I. Gutman, <a href="http://dx.doi.org/10.1016/0893-9659(96)00071-7">The Szeged and the Wiener index of graphs</a>, Appl. Math. Lett., 9, 1996, 45-49.
%H A245827 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A245827 a(n) = (1/2)*n*(17*n^2 - 9).
%F A245827 a(n) = A245826(n, 3).
%F A245827 a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: x*(4*x^2+43*x+4) / (x-1)^4. - _Colin Barker_, Aug 07 2014
%p A245827 a := proc (n) options operator, arrow: (1/2)*n*(17*n^2-9) end proc: seq(a(n), n = 1 .. 40);
%t A245827 CoefficientList[Series[(4 x^2 + 43 x + 4)/(x - 1)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 07 2014 *)
%t A245827 LinearRecurrence[{4,-6,4,-1},{4,59,216,526},40] (* _Harvey P. Dale_, Oct 21 2017 *)
%o A245827 (PARI) Vec(x*(4*x^2+43*x+4)/(x-1)^4 + O(x^100)) \\ _Colin Barker_, Aug 07 2014
%o A245827 (Magma) [(1/2)*n*(17*n^2 - 9): n in [1..40]]; // _Vincenzo Librandi_, Aug 07 2014
%Y A245827 Cf. A245826, A063521, A245828.
%K A245827 nonn,easy
%O A245827 1,1
%A A245827 _Emeric Deutsch_, Aug 06 2014