A245827 Szeged index of the grid graph P_3 X P_n.
4, 59, 216, 526, 1040, 1809, 2884, 4316, 6156, 8455, 11264, 14634, 18616, 23261, 28620, 34744, 41684, 49491, 58216, 67910, 78624, 90409, 103316, 117396, 132700, 149279, 167184, 186466, 207176, 229365, 253084, 278384, 305316, 333931, 364280, 396414, 430384, 466241, 504036, 543820
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- S. Klavzar, A. Rajapakse, I. Gutman, The Szeged and the Wiener index of graphs, Appl. Math. Lett., 9, 1996, 45-49.
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[(1/2)*n*(17*n^2 - 9): n in [1..40]]; // Vincenzo Librandi, Aug 07 2014
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Maple
a := proc (n) options operator, arrow: (1/2)*n*(17*n^2-9) end proc: seq(a(n), n = 1 .. 40);
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Mathematica
CoefficientList[Series[(4 x^2 + 43 x + 4)/(x - 1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 07 2014 *) LinearRecurrence[{4,-6,4,-1},{4,59,216,526},40] (* Harvey P. Dale, Oct 21 2017 *) -
PARI
Vec(x*(4*x^2+43*x+4)/(x-1)^4 + O(x^100)) \\ Colin Barker, Aug 07 2014
Formula
a(n) = (1/2)*n*(17*n^2 - 9).
a(n) = A245826(n, 3).
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