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

1, 1, 2, 7, 26, 71, 258, 857, 3148, 11300, 41841, 154140, 573201, 2129726, 7935779, 29569762, 110281431, 411333271, 1534676318, 5726191937, 21367848168, 79738762725, 297573920356, 1110521036955, 4144432037026, 15467004104026, 57723125759179, 215424338586742, 803971544759711, 3000455162798396, 11197833423648453, 41790839930063492, 155965434740272813, 582070675232252525

Offset

0,3

Comments

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Charles H. Jepsen, Packing a box with bricks, Math. Mag. 64 (2) (1991) 92-97, Table 1.

Index entries for linear recurrences with constant coefficients, signature (6,-4,-26,33,8,-8,24,-31,-14,12,2,-1).

Formula

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) ).

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A109437 (is Jepsen's b(n)/4), A006253 (rigid motion symmetry ignored, Jepsen's a(n)).

Sequence in context: A294681 A229241 A335179 * A091145 A261332 A220304

Adjacent sequences: A387486 A387487 A387488 * A387490 A387491 A387492

Keyword

nonn,easy

Author

R. J. Mathar, Aug 31 2025

Status

approved