login
A320998
Number of pseudo-square convex polyominoes with semiperimeter n.
2
1, 12, 44, 142, 399, 1044, 2571, 6168, 14357, 32786, 73746, 163872, 360462, 786468, 1703949, 3670040, 7864353, 16777260, 35651579, 75497508, 159383591, 335544350, 704643087, 1476395064, 3087007733, 6442451004, 13421772816, 27917287460, 57982058547, 120259084318
OFFSET
6,2
COMMENTS
The offset is not specified but appears to be 6.
LINKS
Srecko Brlek, Andrea Frosini, Simone Rinaldi, and Laurent Vuillon, Tilings by translation: enumeration by a rational language approach, The Electronic Journal of Combinatorics, vol. 13, (2006). See Section 4.2.
FORMULA
a(n) = 2*A045618(6+n) - A320999(n). - Andrew Howroyd, Oct 31 2018
MAPLE
seq(coeff(series(2*x^6/((1-x)^2*(1-2*x)^2)-add(k*x^(3*(k+1))/(1-x^(k+1))^2, k=1..ceil(n/3)), x, n+1), x, n), n = 6 .. 35); # Muniru A Asiru, Oct 31 2018
MATHEMATICA
seq[n_] := 2*x^6/((1 - x)^2*(1 - 2*x)^2) - Sum[k*x^(3*(k + 1))/(1 - x^(k + 1))^2 + O[x]^(6 + n), {k, 1, Ceiling[n/3]}] // CoefficientList[#, x]& // Drop[#, 6]&;
seq[30] (* Jean-François Alcover, Sep 07 2019, from PARI *)
PROG
(PARI) seq(n)={Vec(2*x^6/((1-x)^2*(1-2*x)^2) - sum(k=1, ceil(n/3), k*x^(3*(k+1))/(1-x^(k+1))^2 + O(x^(6+n))))} \\ Andrew Howroyd, Oct 31 2018
CROSSREFS
Sequence in context: A007899 A356322 A100156 * A294521 A309817 A340305
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 30 2018
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Oct 31 2018
STATUS
approved