A320998 Number of pseudo-square convex polyominoes with semiperimeter n.

1, 12, 44, 142, 399, 1044, 2571, 6168, 14357, 32786, 73746, 163872, 360462, 786468, 1703949, 3670040, 7864353, 16777260, 35651579, 75497508, 159383591, 335544350, 704643087, 1476395064, 3087007733, 6442451004, 13421772816, 27917287460, 57982058547, 120259084318

Offset

6,2

Comments

The offset is not specified but appears to be 6.

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

a(n) = 2*A045618(6+n) - A320999(n). - Andrew Howroyd, Oct 31 2018

Maple

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

Mathematica

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]&;
seq[30] (* Jean-François Alcover, Sep 07 2019, from PARI *)

Prog

(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

Crossrefs

Cf. A045618, A320999.

Sequence in context: A343729 A356322 A100156 * A294521 A309817 A340305

Adjacent sequences: A320995 A320996 A320997 * A320999 A321000 A321001

Keyword

nonn

Author

N. J. A. Sloane, Oct 30 2018

Extensions

Terms a(16) and beyond from Andrew Howroyd, Oct 31 2018

Status

approved