Alain Giorgetti has authored 7 sequences.
A239924
Number of unrooted maps with n edges of (orientable) genus 10.
Original entry on oeis.org
380751174738424280720, 123800701289478148878890, 20679270860399513431761798, 2366561529248819497695971912, 208773430159079852919281433050, 15143758135416335992767275804168, 940742579115450773885994408739386
Offset: 20
A239923
Number of unrooted maps with n edges of (orientable) genus 9.
Original entry on oeis.org
324039613564554401, 92075738368876748710, 13524920870667446819490, 1368913666872922446728390, 107367565606418008964576338, 6957847952983327441248445908, 387883525432376769353915075571
Offset: 18
A239922
Number of unrooted maps with n edges of (orientable) genus 8.
Original entry on oeis.org
352755124921122, 86116887841273186, 10954787876407932816, 967146341367928365308, 66599326875830666763353, 3811863659211606517416928, 188710867264106506704457217, 8303453286421604392505856232, 331175730212422476849562734689, 12151338155016475304016716988472
Offset: 16
A239921
Number of unrooted maps with n edges of (orientable) genus 7.
Original entry on oeis.org
508233789579, 104295987346126, 11269592389125547, 852994611088758224, 50777879440443305426, 2531246455428148382456, 109880399953287962099588, 4265557888300762164284822, 150940131172496245801920542, 4938911033961317567088755908, 151101665358744941452325232448
Offset: 14
A239919
Number of unrooted maps with n edges of (orientable) genus 6.
Original entry on oeis.org
1013582110, 169857459866, 15202559941266, 964949198577434, 48695382495936280, 2077641325234343160, 77856954571873092792, 2629247239663140056192, 81498694882848919958250, 2350709723279734060249864, 63759822591543968176310334, 1639827731755812039740785472, 40257891518670970262942165090
Offset: 12
A239918
Number of unrooted maps with n edges of (orientable) genus 5.
Original entry on oeis.org
2976853, 391288854, 28036387466, 1449247494892, 60441165724160, 2158501051914340, 68463726004852884, 1976314846820429680, 52825750657523709792, 1324265997531577820388, 31439565426089264422698, 712298211293218414835136
Offset: 10
A215402
Number of rooted maps of (orientable) genus 4 containing n edges.
Original entry on oeis.org
225225, 24635754, 1495900107, 66519597474, 2416610807964, 75981252764664, 2141204115631518, 55352670009315660, 1334226671709010578, 30347730709395639732, 657304672067357799042, 13652607304062788395788, 273469313030628783700080, 5306599156694095573465824, 100128328831437989131706976, 1842794650155970906232185656
Offset: 8
- Andrew Howroyd, Table of n, a(n) for n = 8..500
- Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], (19-March-2014).
- Steven R. Finch, An exceptional convolutional recurrence, arXiv:2408.12440 [math.CO], 22 Aug 2024.
- Alexander Mednykh, Alain Giorgetti, Enumeration of genus four maps by number of edges, Ars Mathematica Contemporanea 4 (2011), 351--361.
Rooted maps with n edges of genus g for 0 <= g <= 10:
A000168,
A006300,
A006301,
A104742, this sequence,
A238355,
A238356,
A238357,
A238358,
A238359,
A238360.
-
T[0, 0] = 1; T[n_, g_] /; g < 0 || g > n/2 = 0; T[n_, g_] := T[n, g] = ((4 n - 2)/3 T[n - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 T[n - 2, g - 1] + 1/2 Sum[(2 k - 1) (2 (n - k) - 1) T[k - 1, i] T[n - k - 1, g - i], {k, 1, n - 1}, {i, 0, g}])/((n + 1)/6);
a[n_] := T[n, 4];
Table[a[n], {n, 8, 30}] (* Jean-François Alcover, Jul 20 2018 *)
-
A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
A215402_ser(N) = {
my(y=A005159_ser(N+1));
-y*(y-1)^8*(15812*y^12 - 189744*y^11 + 4708549*y^10 - 24892936*y^9 + 173908449*y^8 - 567987942*y^7 + 1743939189*y^6 - 3485359548*y^5 + 5448471852*y^4 - 6051484928*y^3 + 4633500336*y^2 - 2228416192*y + 517976128)/(81*(y-2)^17*(y+2)^10);
};
Vec(A215402_ser(16)) \\ Gheorghe Coserea, Jun 02 2017