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A320998 Number of pseudo-square convex polyominoes with semi-perimeter n. 2
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 (list; graph; refs; listen; history; text; internal format)
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, 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-Fran├žois 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: A296181 A007899 A100156 * A294521 A309817 A194284

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

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Last modified November 26 15:56 EST 2020. Contains 338640 sequences. (Running on oeis4.)