A248094 The hyper-Wiener index of the hexagonal triangle T_n, defined in the He et al. reference.

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

Offset

0,2

Links

Table of n, a(n) for n=0..30.

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 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 42, 444, 2187, 7443, 20247, 47313}, 40] (* Harvey P. Dale, Oct 22 2022 *)

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