Evgeniy Krasko has authored 23 sequences. Here are the ten most recent ones:
A322918
a(n) is the number of rooted 6-regular maps with n vertices on the torus.
Original entry on oeis.org
10, 800, 58000, 4080000, 283100000, 19496000000, 1336380000000, 91320000000000, 6226591000000000, 423871680000000000
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.
A322929
a(n) is the number of rooted 5-regular maps with 2n vertices on the projective plane.
Original entry on oeis.org
215, 106820, 65476730, 44355884860, 31871222091735, 23809740820038860, 18286634336378438820, 14338651143931504204140, 11425366917170617116755180, 9221856681066077433854516240
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.
A322928
a(0)=1; for n>0, a(n) is the number of rooted 3-regular maps with 2n vertices on the projective plane.
Original entry on oeis.org
1, 9, 118, 1773, 28650, 484578, 8457708, 151054173, 2745685954, 50606020854, 943283037684, 17746990547634, 336517405188900, 6423775409047716, 123332141503711704, 2379824766494404317, 46124764901514110898, 897483137740689843054, 17524230350476917414180
Offset: 0
- Valentin Bonzom, Guillaume Chapuy, Maciej Dolega, Enumeration of non-oriented maps via integrability, Alg. Combin. 5 (6) (2022) p 1363-1390, A.3.
- Evgeniy Krasko and Alexander Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics (2019) Vol. 342, Issue 2, 584-599. Also arXiv:1709.03225 [math.CO]. See Th. 3.3 and Table 2.
-
A[0]:= 1: A[1]:= 9: A[2]:= 118: A[3]:= 1773: A[4]:= 28650: A[5]:= 484578:
for n from 6 to 20 do
A[n]:= 995328*(n - 4)*(3*n - 16)*(3*n - 14)*(3*n - 10)*(3*n - 8)*A[n - 6]/((n - 3)*(n - 2)*(n - 1)*n*(n + 1)) - 576*(3*n - 10)*(3*n - 8)*(108*n^2 - 648*n + 1049)*A[n - 4]/((n - 2)*(n - 1)*n*(n + 1)) + 12*(108*n^2 - 432*n + 505)*A[n - 2]/(n*(n + 1))
od:
seq(A[i],i=0..20); # Robert Israel, Dec 30 2022
-
a[n_] := -((2^(2 n + 1) (3 n)!!)/((n + 1)! n!!)) + (3 2^(2 n))/(n + 1)!! Sum[(3^k (2 k - 1)!! (3 n - 2 k - 1)!!)/(2^k k! (n - k)!), {k, 0, n}];
Table[a[n], {n, 0, 20}] (* Andrey Zabolotskiy, Dec 29 2022 *)
Added initial term a(0)=1 to match Taylor series expansion in Theorem 3.3. -
N. J. A. Sloane, Jan 11 2019
A322914
a(0)=0; for n>0, a(n) is the number of rooted 4-regular maps on the torus having n vertices.
Original entry on oeis.org
0, 1, 15, 198, 2511, 31266, 385398, 4721004, 57590271, 700465482, 8501284530, 103007201364, 1246500179910, 15068548264212, 182007001727244, 2196875784339288, 26501619841355871, 319541469851970522, 3851239987536347034, 46399926869155488708, 558853144337650364226
Offset: 0
-
DoubleFactorial:=func< n | &*[n..2 by -2] >; [ 6^(n-1)*(2^n -(DoubleFactorial(2*n-1))/Factorial(n)): n in [0..28] ]; // Vincenzo Librandi, Jan 10 2020
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CoefficientList[Series[(1/6) (1/(1 - 12 x) - 1/Sqrt[1 - 12 x]), {x, 0, 33}], x] (* Vincenzo Librandi, Jan 10 2020 *)
Added initial 0 to match generating function and Taylor series in Theorem 2.1. -
N. J. A. Sloane, Jan 11 2019
A322930
a(n) is the number of rooted 6-regular maps with n vertices on the projective plane.
Original entry on oeis.org
22, 864, 40512, 2075860, 112225776, 6289396632, 361699896960, 21210328632420, 1262859239910000, 76114899842912520
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, Pages 584-599.
A322917
a(n) is the number of rooted 5-regular maps with 2n vertices on the torus.
Original entry on oeis.org
120, 125280, 120800160, 113579366400, 105549958379520, 97452182769223680, 89611995665911173120, 82178813933957614141440, 75217069050598359088496640, 68747100051073934332046868480
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, Pages 584-599.
A297881
Number of unsensed genus 5 maps with n edges.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1491629, 195728778, 14019733828, 724646387874, 30220873171570, 1079253898643492, 34231899372185491, 988157793188200998, 26412878913430197293, 662133032168309300424, 15719783014093104131694
Offset: 0
A297880
Number of unsensed genus 4 maps with n edges.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 7258, 688976, 37466297, 1512650776, 50355225387, 1461269893538, 38236656513725, 922552326544030, 20847359639841664, 446290728182323620, 9129236228868478458, 179639607187998993180, 3418366706444416598777
Offset: 0
A292974
Number of 6-regular maps with n vertices on the torus, up to orientation-preserving isomorphisms.
Original entry on oeis.org
3, 81, 3313, 171282, 9444158, 541659909, 31819176850, 1902508129720, 115307287484560, 7064528615347192, 436658221692698200, 27188662712300575980, 1703444238720524912060
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv preprint arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.
A292972
Number of 5-regular maps with 2n vertices on the torus, up to orientation-preserving isomorphisms.
Original entry on oeis.org
15, 6423, 4031952, 2839677570, 2111005408320, 1624203259187196, 1280171373413389056, 1027235174396893007472, 835745211680299639976976, 687471000510964612782875472
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv preprint arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.