A226301 a(n) = A182107(4n+1).

2, 20, 210, 2460, 31122, 410378, 5575682, 77445152, 1093987598, 15660579168, 226608224226, 3308255447206, 48658330768786, 720224064591558, 10718841444208526, 160283814975116386, 2406806389622598056, 36273856567768931782, 548495166665709003794, 8318227159058988730096

Offset: 1

Author

N. J. A. Sloane, Jun 06 2013

Keywords

• nonn

Links

• Alejandro Erickson, Frank Ruskey, Enumerating maximal tatami mat coverings of square grids with v vertical dominoes, arXiv:1304.0070 [math.CO], 2013.

Crossrefs

Cf. A182107, A226300.

Programs

Mathematica

S[0, 0] = 1; S[0, ] = 0; S[n, k_] /; k < 0 || k > Binomial[n + 1, 2] = 0; S[n_, k_] := S[n, k] = S[n - 1, k] + S[n - 1, k - n];
b[n_] := 2 Sum[Sum[k2 = (n^2 - n)/4 - (n - i - 1) - k1; S[n - i - 2, k1] * S[i - 1, k2], {k1, 0, (n^2 - n)/4 - (n - i - 1)}] + Sum[k2 = (n^2 - n)/4; S[Floor[(n - 2)/2], k1] * S[Floor[(n - 2)/2], k2], {k1, 0, (n^2 - n)/4}], {i, 1, Floor[(n - 1)/2]}];
a[n_] := b[4n+1];
Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Feb 23 2019 *)