login
A320999
Related to the enumeration of pseudo-square convex polyominoes by semiperimeter.
2
1, 0, 2, 2, 3, 0, 11, 0, 5, 10, 12, 0, 20, 0, 25, 16, 9, 0, 51, 12, 11, 22, 39, 0, 69, 0, 46, 28, 15, 38, 104, 0, 17, 34, 105, 0, 105, 0, 67, 92, 21, 0, 175, 30, 82, 46, 81, 0, 141, 66, 159, 52, 27, 0, 299, 0, 29, 140, 144, 80, 177, 0, 109, 64, 213, 0, 374, 0, 35
OFFSET
6,3
COMMENTS
It would be nice to have a more precise definition.
The g.f. is not D-finite.
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
G.f.: Sum_{k>=1} k*x^(3*(k+1))/(1-x^(k+1))^2. - Andrew Howroyd, Oct 31 2018
MAPLE
seq(coeff(series(add(k*x^(3*(k+1))/(1-x^(k+1))^2, k=1..n), x, n+1), x, n), n = 6 .. 75); # Muniru A Asiru, Oct 31 2018
MATHEMATICA
kmax = 80;
Sum[k*x^(3*(k+1))/(1-x^(k+1))^2, {k, 1, kmax}] + O[x]^kmax // CoefficientList[#, x]& // Drop[#, 6]& (* Jean-François Alcover, Sep 10 2019 *)
PROG
(PARI) seq(n)={Vec(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
Cf. A320998.
Sequence in context: A127466 A342314 A099118 * A107098 A293837 A181736
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 30 2018
EXTENSIONS
Terms a(33) and beyond from Andrew Howroyd, Oct 31 2018
STATUS
approved