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 10.
LINKS
Index entries for linear recurrences with constant coefficients, signature (26,176,-146,-14,-140,27).
FORMULA
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).
Recurrence 1:
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),
b(n) = 32*a(n-1) + 9*b(n-1) + 4*c(n-1) + 2*d(n-1) + e(n-1),
c(n) = 52*a(n-1) + 14*b(n-1) + 5*c(n-1) + 4*d(n-1) + 2*e(n-1),
d(n) = 14*a(n-1) + 3*b(n-1) + d(n-1),
e(n) = 48*a(n-1) + 11*b(n-1) + 2*c(n-1) + 2*d(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) = 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.
PROG
(Maxima) /* See A359884. */
CROSSREFS
KEYWORD
nonn
AUTHOR
Gerhard Kirchner, Jan 30 2023
STATUS
approved