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A320999 Related to the enumeration of pseudo-square convex polyominoes by semi-perimeter. 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 (list; graph; refs; listen; history; text; internal format)
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, 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-Fran├žois 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: A199784 A127466 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

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Last modified January 17 11:03 EST 2021. Contains 340228 sequences. (Running on oeis4.)