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A122657 a(n) = if n mod 2 = 1 then (n^2-1)*n^3/4 else n^5/4. 3
0, 0, 8, 54, 256, 750, 1944, 4116, 8192, 14580, 25000, 39930, 62208, 92274, 134456, 189000, 262144, 353736, 472392, 617310, 800000, 1018710, 1288408, 1606044, 1990656, 2437500, 2970344, 3582306, 4302592, 5121690, 6075000, 7149840, 8388608, 9774864, 11358856 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Wiener index of product of two cycles of length n.
LINKS
Eric Weisstein's World of Mathematics, Torus Grid Graph
Eric Weisstein's World of Mathematics, Wiener Index
J. Zerovnik, Szeged index of symmetric graphs, J. Chem. Inf. Comput. Sci., 39 (1999), 77-80.
FORMULA
G.f.: 2*x^2*(4*x^6+19*x^5+62*x^4+70*x^3+62*x^2+19*x+4) /((x+1)^4*(x-1)^6). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009
MATHEMATICA
Table[If[Mod[n, 2] == 0, n^5, (n^2 - 1) n^3]/4, {n, 0, 20}] (* Eric W. Weisstein, May 10 2017 *)
LinearRecurrence[{2, 3, -8, -2, 12, -2, -8, 3, 2, -1}, {0, 8, 54, 256,
750, 1944, 4116, 8192, 14580, 25000}, {0, 20}] (* Eric W. Weisstein, May 10 2017 *)
CoefficientList[Series[2 x^2 (4 x^6 + 19 x^5 + 62 x^4 + 70 x^3 + 62 x^2 + 19 x + 4)/((x + 1)^4 (x - 1)^6), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 08 2017 *)
If[OddQ[#], ((#^2-1)#^3)/4, #^5/4]&/@Range[0, 40] (* Harvey P. Dale, Jul 03 2021 *)
CROSSREFS
Sequence in context: A085540 A259546 A355553 * A152692 A351845 A037966
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 22 2006
STATUS
approved

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Last modified April 16 03:28 EDT 2024. Contains 371696 sequences. (Running on oeis4.)