cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A288278 a(n) is the number of rooted maps with n edges and 8 faces on an orientable surface of genus 4.

Original entry on oeis.org

182231849209410, 24325590127655531, 1587135819804394530, 68503375296263488977, 2221381417843144801098, 58089920897558352891672, 1281537868340178808063824, 24605894500188479477960928, 420612140517667008915254376, 6512251870890866709301451550, 92559480623350598649493386580
Offset: 15

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Author

Gheorghe Coserea, Jun 08 2017

Keywords

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Crossrefs

Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: A288271 f=1, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, this sequence, A288279 f=9, A288280 f=10.
Column 8 of A269924.
Cf. A000108.

Programs

  • Mathematica
    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) ((2n - 1)/3 Q[n - 1, f, g] + (2n - 1)/3 Q[n - 1, f - 1, g] + (2n - 3) (2n - 2) (2n - 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] (2k - 1) (2l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
a[n_] := Q[n, 8, 4];
Table[a[n], {n, 15, 25}] (* Jean-François Alcover, Oct 16 2018 *)

Formula

G.f.: y*(y-1)^15*(2141204115631518*y^14 + 62802256981978404*y^13 + 390904315702808387*y^12 - 17469926941849537*y^11 - 2715522908192830943*y^10 + 1209526054185992549*y^9 + 5862111891800632315*y^8 - 6084780630540788053*y^7 - 1344178041537337418*y^6 + 4359417524034703460*y^5 - 1779344954166712472*y^4 - 128701285301543888*y^3 + 220665627694548576*y^2 - 38233669153240512*y + 844773167217024)/(y-2)^44, where y=A000108(x).

A288279 a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 4.

Original entry on oeis.org

1763184571730010, 258634264294653390, 18451302662846918700, 866831237081712285138, 30468100266480917147760, 860337164444236894357488, 20423544863369526066131328, 420612140517667008915254376, 7689357064107454375292572788, 126977551039680427095997314540, 1920060399356995304343259728312
Offset: 16

Views

Author

Gheorghe Coserea, Jun 08 2017

Keywords

Links

Crossrefs

Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: A288271 f=1, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, this sequence, A288280 f=10.
Column 9 of A269924.
Cf. A000108.

Programs

  • Mathematica
    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) ((2n - 1)/3 Q[n - 1, f, g] + (2n - 1)/3 Q[n - 1, f - 1, g] + (2n - 3) (2n - 2) (2n - 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] (2k - 1) (2l - 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, 4];
Table[a[n], {n, 16, 26}] (* Jean-François Alcover, Oct 16 2018 *)

Formula

G.f.: -6*y*(y-1)^16*(9225445001552610*y^15 + 253889174613116085*y^14 + 1531144661703557241*y^13 - 254390452688914375*y^12 - 11576322921612113581*y^11 + 5646113444605154169*y^10 + 28587502564009313669*y^9 - 31350769849259642447*y^8 - 9832935993984430480*y^7 + 29500732589692418132*y^6 - 12567984363713561312*y^5 - 2218978200544343392*y^4 + 2888444088307833216*y^3 - 630076702195212352*y^2 + 8436883230156800*y + 6263496930404352)/(y-2)^47, where y=A000108(x).

A288280 a(n) is the number of rooted maps with n edges and 10 faces on an orientable surface of genus 4.

Original entry on oeis.org

15894791312284170, 2548272396065512974, 197822824662547694148, 10071757699155275906824, 382217975972687580876304, 11612741439751867739074432, 295680368360952875467454880, 6512251870890866709301451550, 126977551039680427095997314540, 2230836871835420574103711453068
Offset: 17

Views

Author

Gheorghe Coserea, Jun 08 2017

Keywords

Links

Crossrefs

Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: A288271 f=1, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, this sequence.
Column 10 of A269924.
Cf. A000108.

Programs

  • Mathematica
    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) ((2n - 1)/3 Q[n - 1, f, g] + (2n - 1)/3 Q[n - 1, f - 1, g] + (2n - 3) (2n - 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] (2k - 1) (2l - 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, 4];
Table[a[n], {n, 17, 26}] (* Jean-François Alcover, Oct 16 2018 *)

Formula

G.f.: 2*y*(y-1)^17*(667113335854505289*y^16 + 17412039201241985652*y^15 + 101949739105950626070*y^14 - 30202970169901595562*y^13 - 833532476362240891879*y^12 + 447114036864981439647*y^11 + 2316066844919602997013*y^10 - 2673632819222127570107*y^9 - 1088786810085394834566*y^8 + 3157924186313124711792*y^7 - 1371258409341666011952*y^6 - 433458368694714259536*y^5 + 515333809963509426144*y^4 - 126279314363368987008*y^3 - 3637814234318456832*y^2 + 4694513255143047936*y - 365353090019990016)/(y-2)^50, where y=A000108(x).
Previous Showing 11-13 of 13 results.

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