|
|
A360576
|
|
Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes, 2 X 2 X 1 plates and trominos (L-shaped connection of 3 cubes).
|
|
2
|
|
|
1, 6, 122, 1768, 28844, 457592, 7318760, 116806896, 1865305376, 29782666544, 475549098160, 7593154541264, 121241257906000, 1935879286697296, 30910512661708432, 493553365105565264, 7880649886335326608, 125831666350680625104
(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 12.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1-9*x+4*x^2-16*x^3) / (1-15*x-28*x^2+214*x^3-192*x^4-384*x^5+128*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)=15*a(n-1) + 28*a(n-2) - 214*a(n-3) + 192*a(n-4) + 384*a(n-5) - 128*a(n-6)
for n>=6. For n<6, recurrence 1 can be used.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|