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%I #30 May 27 2019 04:05:53
%S 150,536,1336,2712,4826,7840,11916,17216,23902,32136,42080,53896,
%T 67746,83792,102196,123120,146726,173176,202632,235256,271210,310656,
%U 353756,400672,451566,506600,565936,629736,698162,771376,849540,932816,1021366
%N Wiener index of graphs of f.c.c. unit cells in a line = Sum of distances in face-centered cubic grid unit cells connected in a row.
%H Colin Barker, <a href="/A273322/b273322.txt">Table of n, a(n) for n = 1..1000</a>
%H Hamzeh Mujahed, Benedek Nagy, <a href="http://dx.doi.org/10.1107/S2053273315022743">Wiener index on rows of unit cells of the face-centred cubic lattice</a>, Acta Crystallographica, Section A: Foundations and Advances, Volume A72, Part 2 (2016), 243-249.
%H Hamzeh Mujahed, Benedek Nagy, <a href="https://doi.org/0.2478/auom-2018-0011">Exact Formula for Computing the Hyper-Wiener Index on Rows of Unit Cells of the Face-Centred Cubic Lattice</a>, Analele Universitatii Ovidius Constanţa-Seria Matematica Vol. 26(1), 2018, 169-187.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 27*n^3 + 45*n^2 + 62*n + 16.
%F From _Colin Barker_, May 20 2016: (Start)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.
%F G.f.: 2*x*(75 - 32*x + 46*x^2 - 8*x^3) / (1-x)^4.
%F (End)
%t Table[27 n^3 + 45 n^2 + 62 n + 16, {n, 33}] (* or *)
%t Rest@ CoefficientList[Series[2 x (75 - 32 x + 46 x^2 - 8 x^3)/(1 - x)^4, {x, 0, 33}], x] (* _Michael De Vlieger_, May 20 2016 *)
%t LinearRecurrence[{4,-6,4,-1},{150,536,1336,2712},40] (* _Harvey P. Dale_, Dec 04 2018 *)
%o (PARI) Vec(2*x*(75-32*x+46*x^2-8*x^3)/(1-x)^4 + O(x^50)) \\ _Colin Barker_, May 20 2016
%K nonn,easy
%O 1,1
%A _Benedek Nagy_, May 20 2016
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