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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

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

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)