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

6,3

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.

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

Adjacent sequences: A320996 A320997 A320998 * A321000 A321001 A321002

Keyword

nonn

Author

N. J. A. Sloane, Oct 30 2018

Extensions

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

Status

approved