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
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).
Programs
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Magma
[n^4*(n^2-1)/3: n in [1..40]]; // Vincenzo Librandi, Aug 07 2014
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Maple
a := proc (n) options operator, arrow: (1/3)*n^4*(n^2-1) end proc: seq(a(n), n = 1 .. 40);
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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 *)
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)