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

1,1

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).

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

Maple

a := proc (n) options operator, arrow: (1/2)*n*(17*n^2-9) end proc: seq(a(n), n = 1 .. 40);

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 *)

Prog

(PARI) Vec(x*(4*x^2+43*x+4)/(x-1)^4 + O(x^100)) \\ Colin Barker, Aug 07 2014
(Magma) [(1/2)*n*(17*n^2 - 9): n in [1..40]]; // Vincenzo Librandi, Aug 07 2014

Crossrefs

Cf. A245826, A063521, A245828.

Sequence in context: A144992 A198511 A282040 * A200048 A037066 A113251

Adjacent sequences: A245824 A245825 A245826 * A245828 A245829 A245830

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 06 2014

Status

approved