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%I #57 Oct 21 2022 21:25:52
%S 92,377,1128,2700,5548,10227,17392,27798,42300,61853,87512,120432,
%T 161868,213175,275808,351322,441372,547713,672200,816788,983532,
%U 1174587,1392208,1638750,1916668,2228517,2576952,2964728,3394700,3869823,4393152,4967842,5597148
%N Hyper-Wiener index of body-centered cubic grid cells in a row.
%H Colin Barker (Corrected by Harvey P. Dale), <a href="/A302351/b302351.txt">Table of n, a(n) for n = 1..1000</a>
%H Hamzeh Mujahed, Benedek Nagy, <a href="https://dx.doi.org/10.7546/CRABS.2018.05.13">Hyper-Wiener Index on Rows of Unit Cells of the BCC Grid</a>, Comptes rendus de l’Académie bulgare des Sciences, Tome 71, No 5, 2018, 675-684.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (25*n^4 + 105*n^3 + 143*n^2 + 171*n + 108)/6 (proven).
%F From _Colin Barker_, Jun 11 2018: (Start)
%F G.f.: x*(92 - 83*x + 163*x^2 - 90*x^3 + 18*x^4 + 50*x^5 - 250*x^6 + 500*x^7 - 500*x^8 + 250*x^9 - 50*x^10) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>11.
%F (End)
%t Table[(25n^4+105n^3+143n^2+171n+108)/6,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{92,377,1128,2700,5548},40] (* _Harvey P. Dale_, Sep 19 2020 *)
%o (PARI) Vec(x*(92 - 83*x + 163*x^2 - 90*x^3 + 18*x^4 + 50*x^5 - 250*x^6 + 500*x^7 - 500*x^8 + 250*x^9 - 50*x^10) / (1 - x)^5 + O(x^40)) \\ _Colin Barker_, Jun 11 2018
%K nonn,easy
%O 1,1
%A _Benedek Nagy_, Jun 09 2018
%E Corrected and extended by _Harvey P. Dale_, Sep 19 2020
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