Tamas Dekany has authored 2 sequences.
A273988
The number of slim, rectangular lattices of length n>=2.
Original entry on oeis.org
1, 2, 6, 19, 78, 387, 2327, 16384, 132336, 1203145, 12146959, 134749221, 1628840129, 21308361378, 299940041508, 4520381905248, 72625922986869, 1239160455312246, 22377511072312218, 426411855436193451, 8550614540544797370, 179989316790109543775, 3968315581691624472787, 91451247683519227059456
Offset: 2
- Vaclav Kotesovec, Table of n, a(n) for n = 2..400
- Gábor Czédli, Tamás Dékány, Gergő Gyenizse, Júlia Kulin, The number of slim rectangular lattices, Algebra Universalis, 2016, Volume 75, Issue 1, pp 33-50
A273596
For n >= 2, a(n) is the number of slim rectangular diagrams of length n.
Original entry on oeis.org
1, 3, 9, 32, 139, 729, 4515, 32336, 263205, 2401183, 24275037, 269426592, 3257394143, 42615550453, 599875100487, 9040742057760, 145251748024649, 2478320458476795, 44755020000606961, 852823700470009056, 17101229029400788083, 359978633317886558801, 7936631162022905081707
Offset: 2
The initial term is the diagram of the four element diamond shape lattice.
- Vaclav Kotesovec, Table of n, a(n) for n = 2..400
- P. Bala, Notes on A273596
- Gábor Czédli, Tamás Dékány, Gergő Gyenizse, and Júlia Kulin, The number of slim rectangular lattices, Algebra Universalis, 2016, Volume 75, Issue 1, pp 33-50.
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A273596 := proc (n) option remember; `if`(n = 2, 1, `if`(n = 3, 3, (n-2)*procname(n-1) + procname(n-2) + 2)) end: seq(A273596(n), n = 2..20); # Peter Bala, Jan 08 2017
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x = 15;
SRectD = Table[0, {x}];
For[n = 2, n < x, n++,
For[a = 1, a < n, a++,
For[b = 1, b <= n - a, b++,
SRectD[[n]] +=
Binomial[n - a - 1, b - 1]*
Binomial[n - b - 1, a - 1]*(n - a - b)!;
]
]
Print[n, " ", SRectD[[n]]]
]
(* Alternatively: *)
T[n_, k_] := HypergeometricPFQ[{k+1, k-n}, {}, -1];
Table[Sum[T[n,k], {k,0,n}], {n,0,22}] (* Peter Luschny, Oct 05 2017 *)
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a(n)= sum(rps=1, n, sum(r=1, n, s = rps-r; binomial(n-r-1, s-1) * binomial(n-s-1, r-1) * (n-r-s)!)); \\ Michel Marcus, Jun 12 2016
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