Serge Lawrencenko has authored 2 sequences.
A347054
Number of domino tilings of a 32 X n rectangle.
Original entry on oeis.org
1, 1, 3524578, 1117014753, 170220478472105, 224916047725262248, 12348080425980866090537, 30648981125778378496845537, 1010618564986361239515088848178, 3596059736380751648485086101179655, 87171995375835553001398855677616476448, 391978133958466896956216157693001644153072
Offset: 0
- A. M. Magomedov, T. A. Magomedov, S. A. Lawrencenko, Mutually-recursive formulas for enumerating partitions of the rectangle, [in Russian, English summary], Prikl. Diskretn. Mat., 46 (2019), 108-121. DOI: 10.17223/20710410/46/9
- A. M. Magomedov and S. A. Lavrenchenko, Computational aspects of the partition enumeration problem, [in Russian, English summary], Dagestan Electronic Mathematical Reports, 14 (2020), 1-21. DOI: 10.31029/demr.14.1
- M. E. Fisher, Statistical mechanics of dimers on a plane lattice, Phys. Rev., 124 (1961), 1664-1672.
- P. W. Kasteleyn, The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice, Physica, 27 (1961), 1209-1225.
- P. W. Kasteleyn, Dimer statistics and phase transitions, J. Math. Phys., 4 (1963), 287-293.
- V.-H. Nguyen, K. Perrot, M. Vallet, NP-completeness of the game Kingdomino{TM}, Theoret. Comput. Sci., 822 (2020), 23-35.
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Do[ P=1;
Do[P=P*4*(Cos[Pi*i/(n+1)]^2+Cos[Pi*j/33]^2), {i,1,n/2}, {j,1,16}];
Print["n=", n ,":", Round[P]], {n,1,11000}]
A340532
Number of domino tilings of a 16 X n rectangle.
Original entry on oeis.org
1, 1, 1597, 29681, 9475901, 366944287, 69289288909, 3710708201969, 540061286536921, 34741645659770711, 4337452956682508609, 313196612952258199679, 35457442115448212075033, 2764079753958605286860951, 293251198441417290172509377, 24080184063411167042923575793
Offset: 0
a(1) = 1, since there is only one domino tiling of the 16 X n rectangle, which consists entirely of horizontal tiles.
a(2) = 1597 = F(17), since the number of domino tilings of the m X 2 rectangle is the Fibonacci number F(m+1).
Note that the terms a(16) and a(33) are even. More generally, for m even, the numbers of domino tilings of the m X m square and of the m X (2m+1) rectangle are even.
- A. M. Magomedov, T. A. Magomedov, S. A. Lawrencenko, Mutually-recursive formulas for enumerating partitions of the rectangle (Russian, English summary), Prikl. Diskr. Mat., 46 (2019), 108-121.
- Alois P. Heinz, Table of n, a(n) for n = 0..514
- M. E. Fisher, Statistical mechanics of dimers on a plane lattice, Phys. Rev. 124 (1961) 1664-1672.
- P. W. Kasteleyn, The statistics of dimers on a lattice, Physica 27 (1961), 1209-1225.
- P. W. Kasteleyn, Dimer statistics and phase transitions, J. Math. Phys., 4 (1963), 287-293.
- Viet-Ha Nguyen, Kévin Perrot, Mathieu Vallet, NP-completeness of the game Kingdomino(TM), Theoretical Computer Science (2020) Vol. 822, 23-35. See also arXiv:1909.02849, [cs.CC], 2019.
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b:= proc(n, l) option remember; local k;
if n=0 then 1
elif min(l)>0 then (t-> b(n-t, map(h->h-t, l)))(min(l))
else for k while l[k]>0 do od; `if`(n>1, b(n, subsop(k=2, l)), 0)+
`if`(k b(n, [0$16]):
seq(a(n), n=0..15); # Alois P. Heinz, Jan 12 2021
-
Do[
P = 1; m = 16;
Do[
P = N[P*(4*Cos[Pi*i/(n + 1)]^2 + 4*Cos[Pi*j/(m + 1)]^2), 1020],
{i, 1, n/2}, {j, 1, m/2}];
Print["P=", N[P, 1020], " n=", n, " m=", m],
{n, 1, 20}
]
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