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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 Harvey P. Dale, Table of n, a(n) for n = 0..1000 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. Index entries for linear recurrences with constant coefficients, signature (2,3,-8,-2,12,-2,-8,3,2,-1). 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 Cf. A034828, A122658. Sequence in context: A085540 A259546 A355553 * A152692 A351845 A037966 Adjacent sequences: A122654 A122655 A122656 * A122658 A122659 A122660 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.)