OFFSET
0,2
COMMENTS
Hankel transform is 1, 4, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... . - Philippe Deléham, Dec 10 2011
LINKS
David A. Klarner and Spyros S. Magliveras, The number of tilings of a block with blocks, European Journal of Combinatorics 9 (1988), 317-330.
Index entries for linear recurrences with constant coefficients, signature (6,-7).
FORMULA
a(n) = 1+3^(n-1) + Sum_{i=1..n-1} (1+3^(i-1)) a(n-i).
a(n) = 6a(n - 1) - 7a(n - 2), a(n) = ((4 + sqrt(2)) (3 + sqrt(2))^n + (4 - sqrt(2)) (3 - sqrt(2))^n)/14. - N. Sato, May 10 2006
G.f.: (1-x)*(1-3*x)/(1-6*x+7*x^2). - Richard Stanley, Dec 09 2011
E.g.f.: (3 + exp(3*x)*(4*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)))/7. - Stefano Spezia, Feb 17 2022
a(n) = 2*A086351(n-1), n>0. - R. J. Mathar, Apr 07 2022
EXAMPLE
For n=2 the a(2) = 8 ways to cut are:
.___. .___. .___. .___. .___. .___. .___. .___.
| | | | | |___| | |_| |_| | |___| |_|_| |_|_|
|___| |_|_| |___| |_|_| |_|_| |_|_| |___| |_|_| .
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(0) added by Richard Stanley, Dec 09 2011
STATUS
approved