A320999 Related to the enumeration of pseudo-square convex polyominoes by semiperimeter.

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

Author

N. J. A. Sloane, Oct 30 2018

Keywords

• nonn

Comments

It would be nice to have a more precise definition.

The g.f. is not D-finite.

Links

• Andrew Howroyd, Table of n, a(n) for n = 6..1000
• 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.

Crossrefs

Cf. A320998.

Programs

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 *)

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

Formula

G.f.: Sum_{k>=1} k*x^(3*(k+1))/(1-x^(k+1))^2. - Andrew Howroyd, Oct 31 2018

Extensions

Terms a(33) and beyond from Andrew Howroyd, Oct 31 2018