A245828 Szeged index of the grid graph P_n X P_n.

0, 16, 216, 1280, 5000, 15120, 38416, 86016, 174960, 330000, 585640, 988416, 1599416, 2497040, 3780000, 5570560, 8018016, 11302416, 15638520, 21280000, 28523880, 37715216, 49252016, 63590400, 81250000, 102819600, 128963016, 160425216, 198038680, 242730000, 295526720, 357564416, 430094016, 514489360

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

S. Klavzar, A. Rajapakse and I. Gutman, The Szeged and the Wiener index of graphs, Appl. Math. Lett., Vol. 9, No. 5 (1996), pp. 45-49.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = (1/3)*n^4*(n^2 - 1).

G.f.: 8*x^2*(1+x)*(2+11*x+2*x^2)/(1-x)^7.

a(n) = A245826(n,n).

a(n) = 4 * A208954(n).

From Amiram Eldar, Jan 09 2022: (Start)

Sum_{n>=2} 1/a(n) = 33/4 - Pi^2/2 - Pi^4/30.

Sum_{n>=2} (-1)^n/a(n) = 7*Pi^4/240 + Pi^2/4 - 21/4. (End)

Maple

a := proc (n) options operator, arrow: (1/3)*n^4*(n^2-1) end proc: seq(a(n), n = 1 .. 40);

Mathematica

CoefficientList[Series[8 x (1 + x) (2 + 11 x + 2 x^2)/(1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 07 2014 *)
Table[(n^4 (n^2-1))/3, {n, 40}] (* Harvey P. Dale, Mar 25 2021 *)

Prog

(Magma) [n^4*(n^2-1)/3: n in [1..40]]; // Vincenzo Librandi, Aug 07 2014

Crossrefs

Cf. A245826, A208954, A245827.

Sequence in context: A282395 A273588 A125473 * A239096 A269290 A297098

Adjacent sequences: A245825 A245826 A245827 * A245829 A245830 A245831

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 06 2014

Status

approved