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%I #60 Mar 25 2022 09:28:03
%S 1,8,25,52,89,136,193,260,337,424,521,628,745,872,1009,1156,1313,1480,
%T 1657,1844,2041,2248,2465,2692,2929,3176,3433,3700,3977,4264,4561,
%U 4868,5185,5512,5849,6196,6553,6920,7297,7684,8081,8488,8905,9332,9769,10216
%N Number of little cubes visible around an n X n X n cube with a face on a table.
%C There are fewer visible cubes on the bottom than on the top.
%H Leo Tavares, <a href="/A273982/a273982.jpg">Illustration: Diamond Branches</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 5*n^2 - 8*n + 4.
%F a(n) = n^3 - (n-2)^3 - (n-2)^2. - _Joerg Arndt_, Jun 06 2016
%F a(n) = A168668(n-1) + 1. - _Altug Alkan_, Oct 06 2017
%F G.f.: (-1 - 5*x - 4*x^2)/(-1 + x)^3. - _Michael De Vlieger_, Oct 06 2017
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. - _Wesley Ivan Hurt_, Oct 06 2017
%F a(n) = A000566(n-1) + A000566(n), the sum of consecutive heptagonal numbers. - _Charlie Marion_, Jul 01 2021
%F a(n) = n^2 + 4*(n-1)^2. - _Leo Tavares_, Mar 24 2022
%e a(3)=25 because around a 3 X 3 X 3 cube, when it's on a table, it's possible to see only 25 little cubes (8 on each of the 2 bottom layers and 9 on the top layer).
%p A273982:=n->5*n^2-8*n+4: seq(A273982(n), n=1..60); # _Wesley Ivan Hurt_, Oct 06 2017
%t Table[5 n^2 - 8 n + 4, {n, 46}] (* or *)
%t LinearRecurrence[{3, -3, 1}, {1, 8, 25}, 46] (* or *)
%t CoefficientList[Series[(-1 - 5 x - 4 x^2)/(-1 + x)^3, {x, 0, 45}], x] (* _Michael De Vlieger_, Oct 06 2017 *)
%o (Magma) [5*n^2-8*n+4: n in [1..60]]; // _Vincenzo Librandi_, Jun 06 2016
%o (PARI) a(n) = 5*n^2 - 8*n + 4; \\ _Altug Alkan_, Oct 06 2017
%Y Cf. A005897, A168668, A000566.
%K nonn,easy
%O 1,2
%A _Sébastien Dumortier_, Jun 05 2016
%E a(2) corrected and entry edited by _Andrey Zabolotskiy_, Oct 06 2017
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