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A360222 a(n) is the number of permutable pieces in a standard n X n X n Rubik's cube.

%I A360222 #28 Oct 04 2024 15:41:36
%S A360222 0,8,20,56,92,152,212,296,380,488,596,728,860,1016,1172,1352,1532,
%T A360222 1736,1940,2168,2396,2648,2900,3176,3452,3752,4052,4376,4700,5048,
%U A360222 5396,5768,6140,6536,6932,7352,7772,8216,8660,9128,9596,10088,10580,11096,11612,12152
%N A360222 a(n) is the number of permutable pieces in a standard n X n X n Rubik's cube.
%H A360222 Paolo Xausa, <a href="/A360222/b360222.txt">Table of n, a(n) for n = 1..10000</a>
%H A360222 <a href="/index/Ru#Rubik">Index entries for sequences related to Rubik cube</a>
%H A360222 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A360222 a(n) = 8 + 12*(n-2) + 6*((n-2)^2 - (n mod 2)) for n > 1, a(1) = 0.
%F A360222 G.f.: 4*x^2*(x^3-4*x^2-x-2)/((x+1)*(x-1)^3).
%F A360222 a(n) = A005897(n-1) - A010677(n) for n>=2.
%F A360222 E.g.f.: 2*(2*(x - 2) + (3*x^2 - 3*x + 4)*cosh(x) + (3*x^2 - 3*x + 1)*sinh(x)). - _Stefano Spezia_, Feb 02 2023
%e A360222 The 2 X 2 X 2 Rubik's cube consists of 8 corner pieces, so a(2) = 8; the 3 X 3 X 3 cube has 8 corner pieces, 12 edge pieces, and 6 non-permutable center pieces, so a(3) = 8 + 12 = 20.
%t A360222 A360222[n_] := If[n == 1, 0, 6*((n-2)*n - Mod[n, 2]) + 8]; Array[A360222, 50] (* or *)
%t A360222 LinearRecurrence[{2, 0, -2, 1}, {0, 8, 20, 56, 92}, 50] (* _Paolo Xausa_, Oct 04 2024 *)
%o A360222 (Python)
%o A360222 N = 20
%o A360222 seq = [0]
%o A360222 for n in range(2, N+1):
%o A360222    seq.append( 8 + 12*(n-2) + 6*((n-2)**2 - (n%2)) )
%Y A360222 Cf. A005897, A010677.
%K A360222 nonn,easy
%O A360222 1,2
%A A360222 _William Riley Barker_, Jan 30 2023