A288089
a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 2.
Original entry on oeis.org
1293938646, 140725699686, 7454157823560, 261637840342860, 6928413234959820, 148755268498286436, 2710382626755160416, 43241609165618454096, 617910462111714896820, 8044640800289827566756, 96690983139765469347024, 1084226645505246141589704, 11439196912435362172792536, 114351801899024314438876200
Offset: 12
-
Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
Q[n_, f_, g_] := Q[n, f, g] = 6/(n + 1) ((2 n - 1)/3 Q[n - 1, f, g] + (2 n - 1)/3 Q[n - 1, f - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 Q[n - 2, f, g - 1] + 1/2 Sum[l = n - k; Sum[v = f - u; Sum[j = g - i; Boole[l >= 1 && v >= 1 && j >= 0] (2 k - 1) (2 l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
a[n_] := Q[n, 9, 2];
Table[a[n], {n, 12, 25}] (* Jean-François Alcover, Oct 18 2018 *)
-
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288089_ser(N) = {
my(y = A000108_ser(N+1));
-6*y*(y-1)^12*(12205186004*y^11 + 144345246789*y^10 + 83883548039*y^9 - 978172313331*y^8 + 436600889944*y^7 + 1435650005364*y^6 - 1511798886368*y^5 + 121539026592*y^4 + 411304907520*y^3 - 171035694144*y^2 + 14120686592*y + 1573053440)/(y-2)^35;
};
Vec(A288089_ser(13))
A288090
a(n) is the number of rooted maps with n edges and 10 faces on an orientable surface of genus 2.
Original entry on oeis.org
7808250450, 955708437684, 56532447160536, 2200626948631386, 64232028100704156, 1511718920778951024, 30044423965980553536, 520516978029736518606, 8044640800289827566756, 112860842135424498808968, 1456882832375987896763184, 17491588653334242501297012, 197038603477850885815215480
Offset: 13
-
Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
Q[n_, f_, g_] := Q[n, f, g] = 6/(n + 1) ((2 n - 1)/3 Q[n - 1, f, g] + (2 n - 1)/3 Q[n - 1, f - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 Q[n - 2, f, g - 1] + 1/2 Sum[l = n - k; Sum[v = f - u; Sum[j = g - i; Boole[l >= 1 && v >= 1 && j >= 0] (2 k - 1) (2 l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
a[n_] := Q[n, 10, 2];
Table[a[n], {n, 13, 25}] (* Jean-François Alcover, Oct 18 2018 *)
-
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288090_ser(N) = {
my(y = A000108_ser(N+1));
6*y*(y-1)^13*(197300616213*y^12 + 2233379349250*y^11 + 1077980722075*y^10 - 16537713992125*y^9 + 7856375825902*y^8 + 29387232350368*y^7 - 33290642716432*y^6 + 994024496848*y^5 + 14078465181600*y^4 - 6737013421440*y^3 + 532103069696*y^2 + 244607984896*y - 34798091776)/(y-2)^38;
};
Vec(A288090_ser(13))
A006299
Number of rooted genus-2 maps with n edges.
Original entry on oeis.org
21, 483, 15018, 258972, 5554188, 85421118, 1558792200, 22555934280, 375708427812, 5235847653036, 82234427131416, 1117259292848016, 16842445235560944, 224686278407291148, 3286157560248860532, 43241609165618454096, 617910462111714896820
Offset: 4
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.