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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. 2
1, 8, 153, 2470, 41571, 693850, 11602579, 193942076, 3242104149, 54196828452, 905988148597, 15145052657186, 253174020910071, 4232212575080006, 70748267813548207, 1182671546039152712, 19770264765434877913, 330491902143708738464 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
LINKS
FORMULA
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).
Recurrence 1:
a(n) = 8*a(n-1) + 3*b(n-1) + 2*c(n-1) + d(n-1) + e(n-1) + 7*a(n-2)
b(n) = 12*a(n-1) + 5*b(n-1) + 2*c(n-1) + 2*d(n-1) + e(n-1)
c(n) = 16*a(n-1) + 4*b(n-1) + 2*c(n-1)
d(n) = 2*a(n-1) + b(n-1) + d(n-1)
e(n) = 12*a(n-1) + 3*b(n-1)
with a(n),b(n),c(n),d(n),e(n)= 0 for n<=0 except for a(0)=1.
Recurrence 2:
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)
for n>=6. For n<6, recurrence 1 can be used.
CROSSREFS
Sequence in context: A094059 A171202 A247538 * A304400 A174845 A352253
KEYWORD
nonn
AUTHOR
Gerhard Kirchner, Feb 12 2023
STATUS
approved

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Last modified July 15 23:38 EDT 2024. Contains 374343 sequences. (Running on oeis4.)