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 A248094 The hyper-Wiener index of the hexagonal triangle T_n, defined in the He et al. reference. 1
 0, 42, 444, 2187, 7443, 20247, 47313, 98994, 190386, 342576, 584034, 952149, 1494909, 2272725, 3360399, 4849236, 6849300, 9491814, 12931704, 17350287, 22958103, 29997891, 38747709, 49524198, 62685990, 78637260, 97831422, 120774969, 148031457, 180225633, 218047707 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Q. H. He, J. Z. Gu, S. J. Xu, and W. H. Chan, Hosoya polynomials of hexagonal triangles and trapeziums, MATCH, Commun. Math. Comput. Chem. 72, 2014, 835-843. Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA a(n) = n*(66 + 407n + 670n^2 + 425n^3 + 104n^4 + 8n^5)/40 (see Corollary 3,10 in the He et al. reference). G.f.: z*(42+150*z-39*z^2-12*z^3+3*z^4) /(1-z)^7. (Corrected by Vincenzo Librandi, Nov 15 2014) a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 6. - Wesley Ivan Hurt, Aug 16 2016 MAPLE a := n -> (1/40)*n*(66 + 407*n + 670*n^2 + 425*n^3 + 104*n^4 + 8*n^5): seq(a(n), n = 0 .. 30); MATHEMATICA CoefficientList[Series[x (42 + 150 x - 39 x^2 - 12 x^3 + 3 x^4) / (1 - x)^7, {x, 0, 30}], x] (* Vincenzo Librandi, Nov 15 2014 *) PROG (MAGMA) [n*(66+407*n+670*n^2+425*n^3+104*n^4+8*n^5)/40: n in [0..30]]; // Vincenzo Librandi, Nov 15 2014 CROSSREFS Cf. A033544, A248093. Sequence in context: A230933 A231110 A156762 * A244909 A090297 A008387 Adjacent sequences:  A248091 A248092 A248093 * A248095 A248096 A248097 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Nov 14 2014 STATUS approved

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Last modified July 25 13:05 EDT 2021. Contains 346290 sequences. (Running on oeis4.)