OFFSET
0,3
COMMENTS
Triangles only occur as pairs forming 2 X 2 squares. For program code and additional details, see A362297.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,18,-48,-42,99).
FORMULA
a(n) = 4*a(n-1) + 18*a(n-2) - 48*a(n-3) - 42*a(n-4) + 99*a(n-5).
G.f.: (9*x^3-3*x^2-3*x+1)/(-99*x^5+42*x^4+48*x^3-18*x^2-4*x+1).
EXAMPLE
a(2) = 19.
Partitions of a 2 X 2 square (triangles or dominos):
___ ___ ___ ___
| /| |\ | |___| | | |
|/__| |__\| |___| |_|_|
2t 2d
___ ___ ___ ___ ___ ___ _ ___ _ _______
|2t |2t | |2t |2d | |2d |2t | | |2t | | |only d |
|___|___| |___|___| |___|___| |_|___|_| |_______|
4 ways + 4 ways + 4 ways + 2 ways + 5 ways = 19 ways
Only dominos: A005178(3) = 5.
MATHEMATICA
LinearRecurrence[{4, 18, -48, -42, 99}, {1, 1, 19, 55, 472}, 24] (* Stefano Spezia, Apr 20 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gerhard Kirchner, Apr 19 2023
STATUS
approved