OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,1,4,2).
FORMULA
a(n) = a(n-1) + a(n-2) + 4*a(n-3) + 2*a(n-4).
Sum_{j=0..n} a(n) = (1/7)(a(n+4) - a(n+2) - 5*a(n+1) - 1).
G.f.: 1/(1 - x - x^2 - 4*x^3 - 2*x^4). - Stefano Spezia, Jun 19 2021
a(n) = F(n+1) + 2*Sum_{j=3..n} a(n-j)*F(j) for F(i) = A000045(i) the i-th Fibonacci number. - Greg Dresden, Nov 10 2024
EXAMPLE
For n = 3 the a(3)=7 tilings are:
._____. ._____. ._____. ._____.
| |___| |___| | | ___| |___ |
|_____| |_____| |_|___| |___|_|
._____. ._____. ._____.
|___| | | |___| | | | |
|___|_| |_|___| |_|_|_|
MATHEMATICA
LinearRecurrence[{1, 1, 4, 2}, {1, 1, 2, 7}, 40]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Greg Dresden and Yiwen Zhang, Jun 19 2021
STATUS
approved