A288028 Number of maximal matchings in the grid graph P_3 X P_n.

2, 5, 22, 75, 264, 941, 3286, 11623, 40960, 144267, 508812, 1792981, 6319994, 22277291, 78518760, 276763545, 975517878, 3438444583, 12119670866, 42718700667, 150572583140, 530730064095, 1870688029160, 6593699432859, 23241110692298, 81918995835971

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Svenja Huntemann, Neil A. McKay, Counting Domineering Positions, arXiv:1909.12419 [math.CO], 2019.

Formula

Empirical: a(n) = a(n-1) +5*a(n-2) +11*a(n-3) +5*a(n-4) +14*a(n-5) +8*a(n-6) +3*a(n-7) -5*a(n-9) -11*a(n-10) -a(n-11) +2*a(n-12) +a(n-15) for n>15.

Empirical g.f.: x*(2 +3*x +7*x^2 +6*x^3 +14*x^4 +7*x^5 +4*x^6 -x^7 -5*x^8 - 11*x^9 -2*x^10 +2*x^11 +x^12 +x^14)/(1 -x -5*x^2 -11*x^3 -5*x^4 -14*x^5 - 8*x^6 -3*x^7 +5*x^9 +11*x^10 +x^11 -2*x^12 -x^15). - Colin Barker, Jun 11 2017

Crossrefs

Row 3 of A288026.

Cf. A286945, A287595.

Sequence in context: A041165 A041006 A346557 * A083465 A339646 A215100

Adjacent sequences: A288025 A288026 A288027 * A288029 A288030 A288031

Keyword

nonn

Author

Andrew Howroyd, Jun 04 2017

Status

approved