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

%I A248094 #24 Oct 22 2022 09:25:42
%S A248094 0,42,444,2187,7443,20247,47313,98994,190386,342576,584034,952149,
%T A248094 1494909,2272725,3360399,4849236,6849300,9491814,12931704,17350287,
%U A248094 22958103,29997891,38747709,49524198,62685990,78637260,97831422,120774969,148031457,180225633,218047707
%N A248094 The hyper-Wiener index of the hexagonal triangle T_n, defined in the He et al. reference.
%H A248094 Q. H. He, J. Z. Gu, S. J. Xu, and W. H. Chan, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match72/n3/match72n3_835-843.pdf">Hosoya polynomials of hexagonal triangles and trapeziums</a>, MATCH, Commun. Math. Comput. Chem. 72, 2014, 835-843.
%H A248094 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A248094 a(n) = n*(66 + 407n + 670n^2 + 425n^3 + 104n^4 + 8n^5)/40 (see Corollary 3,10 in the He et al. reference).
%F A248094 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)
%F A248094 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
%p A248094 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);
%t A248094 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 *)
%t A248094 LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,42,444,2187,7443,20247,47313},40] (* _Harvey P. Dale_, Oct 22 2022 *)
%o A248094 (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
%Y A248094 Cf. A033544, A248093.
%K A248094 nonn,easy
%O A248094 0,2
%A A248094 _Emeric Deutsch_, Nov 14 2014