A320999 - OEIS

%I #23 Feb 08 2024 08:48:52

%S 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,

%T 28,15,38,104,0,17,34,105,0,105,0,67,92,21,0,175,30,82,46,81,0,141,66,

%U 159,52,27,0,299,0,29,140,144,80,177,0,109,64,213,0,374,0,35

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

%C It would be nice to have a more precise definition.

%C The g.f. is not D-finite.

%H Andrew Howroyd, <a href="/A320999/b320999.txt">Table of n, a(n) for n = 6..1000</a>

%H Srecko Brlek, Andrea Frosini, Simone Rinaldi, and Laurent Vuillon, <a href="https://doi.org/10.37236/1041">Tilings by translation: enumeration by a rational language approach</a>, The Electronic Journal of Combinatorics, vol. 13, (2006). See Section 4.2.

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

%p 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

%t kmax = 80;

%t 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 *)

%o (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

%Y Cf. A320998.

%K nonn

%O 6,3

%A _N. J. A. Sloane_, Oct 30 2018

%E Terms a(33) and beyond from _Andrew Howroyd_, Oct 31 2018