cp's OEIS Frontend

A360066 Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes, 2 X 1 X 1 dominos and trominos (L-shaped connection of 3 cubes).

%I A360066 #16 Mar 03 2024 17:17:41
%S A360066 1,11,444,13311,422617,13265660,417336617,13123557903,412719195520,
%T A360066 12979269602143,408175860119021,12836425011761592,403683424226081169,
%U A360066 12695147020245034099,399240466722076292612,12555423726269799691295,394846409914451855949249
%N A360066 Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes, 2 X 1 X 1 dominos and trominos (L-shaped connection of 3 cubes).
%C A360066 Recurrence 1 is derived in A359884, "3d-tilings of a 2 X 2 X n box" as a special case of a more general tiling problem: III, example 10.
%H A360066 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (26,176,-146,-14,-140,27).
%F A360066 G.f.: (1 - 15*x - 18*x^2 - 23*x^3 + 7*x^4) / (1 - 26*x - 176*x^2 + 146*x^3 + 14*x^4 + 140*x^5 - 27*x^6).
%F A360066 Recurrence 1:
%F A360066 a(n) = 11*a(n-1) + 4*b(n-1) + 2*c(n-1) + d(n-1) + e(n-1) + 29*a(n-2) + 6*b(n-2) + c(n-2) + 2*d(n-2),
%F A360066 b(n) = 32*a(n-1) + 9*b(n-1) + 4*c(n-1) + 2*d(n-1) + e(n-1),
%F A360066 c(n) = 52*a(n-1) + 14*b(n-1) + 5*c(n-1) + 4*d(n-1) + 2*e(n-1),
%F A360066 d(n) = 14*a(n-1) + 3*b(n-1) + d(n-1),
%F A360066 e(n) = 48*a(n-1) + 11*b(n-1) + 2*c(n-1) + 2*d(n-1),
%F A360066 with a(n), b(n), c(n), d(n), e(n) = 0 for n <= 0 except for a(0)=1.
%F A360066 Recurrence 2:
%F A360066 a(n) = 26*a(n-1) + 176*a(n-2) - 146*a(n-3) - 14*a(n-4) - 140*a(n-5) + 27*a(n-6) for n >= 6. For n < 6, recurrence 1 can be used.
%o A360066 (Maxima) /* See A359884. */
%Y A360066 Cf. A006253, A001045, A033516, A335559, A359884, A359885, A360064, A360065.
%K A360066 nonn
%O A360066 0,2
%A A360066 _Gerhard Kirchner_, Jan 30 2023