A082679 Number of LEGO towers, one piece per floor, where every floor is perpendicular to the one below it (so we have a kind of 3-dimensional zigzag pattern).

0, 1, 2, 6, 20, 69, 241, 845, 2966, 10414, 36568, 128409, 450913, 1583401, 5560186, 19524854, 68562444, 240760253, 845440977, 2968805845, 10425101678, 36608235998, 128551546480, 451414815601, 1585164405441

Offset

0,3

Links

Table of n, a(n) for n=0..24.

D. Zeilberger, [math/9801016] Automated counting of LEGO towers

Index entries for linear recurrences with constant coefficients, signature (5,-6,3,-1).

Formula

G.f.: x*(1 - 3*x + 2*x^2 - x^3)/(1 - 5*x + 6*x^2 - 3*x^3 + x^4).

Mathematica

CoefficientList[Series[x*(1 - 3*x + 2*x^2 - x^3)/(1 - 5*x + 6*x^2 - 3*x^3 + x^4), {x, 0, 30}], x] (* Wesley Ivan Hurt, Feb 12 2017 *)
LinearRecurrence[{5, -6, 3, -1}, {0, 1, 2, 6, 20}, 30] (* Harvey P. Dale, Nov 10 2021 *)

Crossrefs

Sequence in context: A150121 A150122 A150123 * A094854 A217782 A026029

Adjacent sequences: A082676 A082677 A082678 * A082680 A082681 A082682

Keyword

nonn,easy

Author

Ralf Stephan, May 19 2003

Status

approved