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

Author

Ralf Stephan, May 19 2003

Keywords

• nonn
• easy

Links

• D. Zeilberger, [math/9801016] Automated counting of LEGO towers
• Index entries for linear recurrences with constant coefficients, signature (5,-6,3,-1).

Programs

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 *)

Formula

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