cp's OEIS Frontend

A360575 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 2 X 2 X 1 plates.

%I A360575 #7 Feb 13 2023 03:10:50
%S A360575 1,8,153,2470,41571,693850,11602579,193942076,3242104149,54196828452,
%T A360575 905988148597,15145052657186,253174020910071,4232212575080006,
%U A360575 70748267813548207,1182671546039152712,19770264765434877913,330491902143708738464
%N A360575 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 2 X 2 X 1 plates.
%C A360575 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 11.
%H A360575 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (16,21,-157,100,65,-42).
%F A360575 G.f.: (1-8*x+4*x^2+11*x^3-6*x^4) / (1-16*x-21*x^2+157*x^3-100*x^4-65*x^5+42*x^6).
%F A360575 Recurrence 1:
%F A360575 a(n) = 8*a(n-1) + 3*b(n-1) + 2*c(n-1) + d(n-1) + e(n-1) + 7*a(n-2)
%F A360575 b(n) = 12*a(n-1) + 5*b(n-1) + 2*c(n-1) + 2*d(n-1) + e(n-1)
%F A360575 c(n) = 16*a(n-1) + 4*b(n-1) + 2*c(n-1)
%F A360575 d(n) = 2*a(n-1) + b(n-1) + d(n-1)
%F A360575 e(n) = 12*a(n-1) + 3*b(n-1)
%F A360575 with a(n),b(n),c(n),d(n),e(n)= 0 for n<=0 except for a(0)=1.
%F A360575 Recurrence 2:
%F A360575 a(n)=16*a(n-1) + 21*a(n-2) - 157*a(n-3) + 100*a(n-4) + 65*a(n-5) - 42*a(n-6)
%F A360575 for n>=6. For n<6, recurrence 1 can be used.
%Y A360575 Cf. A006253, A001045, A033516, A335559, A359884, A359885, A360064, A360065, A360576, A360577.
%K A360575 nonn
%O A360575 0,2
%A A360575 _Gerhard Kirchner_, Feb 12 2023