OFFSET
1,6
COMMENTS
A U-frame polyomino has a perimeter that forms a self-avoiding polygon such that as you traverse the perimeter counterclockwise you encounter turns in the order LLLLLLRR.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: Sum_{k>=1} (x^k/(1 - x^k)) * (B(k+1, x)^2 + B(k+1, x^2))/2 where B(k, x) = Sum_{j>=k} x^j/(1 - x^j). - Andrew Howroyd, Feb 07 2023
EXAMPLE
a(5)=1 because of:
OO
O
OO
The a(7) = 5 polyominoes are:
O
O O O O
O O O O O OO O O O O
OOO OOO OOOO OOOO OOOOO
PROG
(PARI) B(n, k, x) = sum(j=k, n, x^j/(1 - x^j), O(x*x^n))
seq(n) = Vec(sum(k=1, (n-2)\3, x^k*(B(n-k, k+1, x)^2 + B((n-k)\2, k+1, x^2))/(1-x^k), O(x*x^n))/2, -n) \\ Andrew Howroyd, Feb 07 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
John Mason, Feb 06 2023
STATUS
approved