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
Index entries for linear recurrences with constant coefficients, signature (16,21,-157,100,65,-42).
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
KEYWORD
nonn
AUTHOR
Gerhard Kirchner, Feb 12 2023
STATUS
approved