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%I #29 Jan 04 2021 19:29:24
%S 64,206,488,960,1672,2674,4016,5748,7920,10582,13784,17576,22008,
%T 27130,32992,39644,47136,55518,64840,75152,86504,98946,112528,127300,
%U 143312,160614,179256,199288,220760,243722,268224,294316,322048,351470,382632,415584,450376,487058,525680,566292
%N Wiener index of graph of b.c.c. unit cells in a line = Sum of distances in a b.c.c. row graph.
%H Colin Barker, <a href="/A273321/b273321.txt">Table of n, a(n) for n = 1..1000</a>
%H Hamzeh Mujahed, Benedek Nagy, <a href="http://dx.doi.org/10.1007/978-3-319-18720-4_50">Wiener Index on Lines of Unit Cells of the Body-Centered Cubic Grid</a>, Mathematical Morphology and Its Applications to Signal and Image Processing, Volume 9082 of the series Lecture Notes in Computer Science, pp. 597-606.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (25/3)*n^3 + 20*n^2 + (71/3)*n + 12.
%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 O.g.f.: 2*x*(32 - 25*x + 24*x^2 - 6*x^3) / (1 - x)^4. (End)
%F E.g.f.: (12 + 52*x + 45*x^2 + (25/3)*x^3)*exp(x) - 12. - _Benedict W. J. Irwin_, May 27 2016
%t Table[(25/3) n^3 + 20 n^2 + (71/3) n + 12, {n, 40}] (* or *)
%t Rest@ CoefficientList[Series[2 x (32 - 25 x + 24 x^2 - 6 x^3)/(1 - x)^4, {x, 0, 40}], x] (* _Michael De Vlieger_, May 20 2016 *)
%o (PARI) Vec(2*x*(32-25*x+24*x^2-6*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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