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A387489 Number of packing 1X1X2 bricks into 2X2Xn boxes considering packings obtained by rigid motions equivalent.

%I A387489 #15 Sep 02 2025 14:10:56
%S A387489 1,1,2,7,26,71,258,857,3148,11300,41841,154140,573201,2129726,7935779,
%T A387489 29569762,110281431,411333271,1534676318,5726191937,21367848168,
%U A387489 79738762725,297573920356,1110521036955,4144432037026,15467004104026,57723125759179,215424338586742,803971544759711,3000455162798396,11197833423648453,41790839930063492,155965434740272813,582070675232252525
%N A387489 Number of packing 1X1X2 bricks into 2X2Xn boxes considering packings obtained by rigid motions equivalent.
%C A387489 There seem to be several typos in Jepsen's equations. The enumeration here is derived from the expression of p(n) as 1/8ths of Psi(e)+2*Psi(rho)+Psi(rho^2)+2*Psi(sigma)+2*Psi(rho*sigma) if n>=3.
%H A387489 Vincenzo Librandi, <a href="/A387489/b387489.txt">Table of n, a(n) for n = 0..1000</a>
%H A387489 Charles H. Jepsen, <a href="https://doi.org/10.2307/2690755">Packing a box with bricks</a>, Math. Mag. 64 (2) (1991) 92-97, Table 1.
%H A387489 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (6,-4,-26,33,8,-8,24,-31,-14,12,2,-1).
%F A387489 G.f.: 1 +x +2*x^2 -x^3*(-7 +16*x +57*x^2 -118*x^3 -38*x^4 +30*x^5 -53*x^6 +127*x^7 +42*x^8 -49*x^9 -7*x^10 +4*x^11) / ( (x-1)*(1+x) *(x^2+2*x-1) *(x^2+1) *(x^2-4*x+1) *(x^4-4*x^2+1) ).
%t A387489 CoefficientList[Series[1+x+2*x^2-x^3*(-7+16*x+57*x^2-118*x^3-38*x^4+30*x^5-53*x^6+127*x^7+42*x^8-49*x^9-7*x^10+4*x^11)/((x-1)*(1+x)*(x^2+2*x-1)*(x^2+1)*(x^2-4*x+1)*(x^4-4*x^2+1)),{x,0,33}],x] (* _Vincenzo Librandi_, Sep 02 2025 *)
%o A387489 (Magma) m:=35; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1 +x +2*x^2 -x^3*(-7 +16*x +57*x^2 -118*x^3 -38*x^4 +30*x^5 -53*x^6 +127*x^7 +42*x^8 -49*x^9 -7*x^10 +4*x^11) / ( (x-1)*(1+x) *(x^2+2*x-1) *(x^2+1) *(x^2-4*x+1) *(x^4-4*x^2+1)) )); // _Vincenzo Librandi_, Sep 02 2025
%Y A387489 Cf. A109437 (is Jepsen's b(n)/4), A006253 (rigid motion symmetry ignored, Jepsen's a(n)).
%K A387489 nonn,easy,new
%O A387489 0,3
%A A387489 _R. J. Mathar_, Aug 31 2025