A320998 - OEIS

%I #24 Feb 08 2024 08:47:38

%S 1,12,44,142,399,1044,2571,6168,14357,32786,73746,163872,360462,

%T 786468,1703949,3670040,7864353,16777260,35651579,75497508,159383591,

%U 335544350,704643087,1476395064,3087007733,6442451004,13421772816,27917287460,57982058547,120259084318

%N Number of pseudo-square convex polyominoes with semiperimeter n.

%C The offset is not specified but appears to be 6.

%H Andrew Howroyd, <a href="/A320998/b320998.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 a(n) = 2*A045618(6+n) - A320999(n). - _Andrew Howroyd_, Oct 31 2018

%p seq(coeff(series(2*x^6/((1-x)^2*(1-2*x)^2)-add(k*x^(3*(k+1))/(1-x^(k+1))^2,k=1..ceil(n/3)),x,n+1), x, n), n = 6 .. 35); # _Muniru A Asiru_, Oct 31 2018

%t seq[n_] := 2*x^6/((1 - x)^2*(1 - 2*x)^2) - Sum[k*x^(3*(k + 1))/(1 - x^(k + 1))^2 + O[x]^(6 + n), {k, 1, Ceiling[n/3]}] // CoefficientList[#, x]& // Drop[#, 6]&;

%t seq[30] (* _Jean-François Alcover_, Sep 07 2019, from PARI *)

%o (PARI) seq(n)={Vec(2*x^6/((1-x)^2*(1-2*x)^2) - 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. A045618, A320999.

%K nonn

%O 6,2

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

%E Terms a(16) and beyond from _Andrew Howroyd_, Oct 31 2018