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

%I A320999 #23 Feb 08 2024 08:48:52
%S A320999 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 A320999 28,15,38,104,0,17,34,105,0,105,0,67,92,21,0,175,30,82,46,81,0,141,66,
%U A320999 159,52,27,0,299,0,29,140,144,80,177,0,109,64,213,0,374,0,35
%N A320999 Related to the enumeration of pseudo-square convex polyominoes by semiperimeter.
%C A320999 It would be nice to have a more precise definition.
%C A320999 The g.f. is not D-finite.
%H A320999 Andrew Howroyd, <a href="/A320999/b320999.txt">Table of n, a(n) for n = 6..1000</a>
%H A320999 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 A320999 G.f.: Sum_{k>=1} k*x^(3*(k+1))/(1-x^(k+1))^2. - _Andrew Howroyd_, Oct 31 2018
%p A320999 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 A320999 kmax = 80;
%t A320999 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 A320999 (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 A320999 Cf. A320998.
%K A320999 nonn
%O A320999 6,3
%A A320999 _N. J. A. Sloane_, Oct 30 2018
%E A320999 Terms a(33) and beyond from _Andrew Howroyd_, Oct 31 2018