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.

Showing 1-10 of 10 results.

A269925 Triangle read by rows: T(n,f) is the number of rooted maps with n edges and f faces on an orientable surface of genus 5.

Original entry on oeis.org

59520825, 4304016990, 4304016990, 158959754226, 354949166565, 158959754226, 4034735959800, 14805457339920, 14805457339920, 4034735959800, 79553497760100, 420797306522502, 691650582088536, 420797306522502, 79553497760100, 1302772718028600, 9220982517965400, 21853758736216200, 21853758736216200, 9220982517965400, 1302772718028600
Offset: 10

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Author

Gheorghe Coserea, Mar 15 2016

Keywords

Comments

Row n contains n-9 terms.

Examples

			Triangle starts:
n\f  [1]             [2]             [3]             [4]
[10] 59520825;
[11] 4304016990,     4304016990;
[12] 15895975422,    354949166565,   158959754226;
[13] 4034735959800,  14805457339920, 14805457339920, 4034735959800;
[14] ...

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
Row sums give A238355 (column 5 of A269919).
Cf. A035309, A269921, A269922, A269923, A269924, A270406, A270407, A270408, A270409, A270410, A270411, A270412.

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}]);
Table[Q[n, f, 5], {n, 10, 15}, {f, 1, n-9}] // Flatten (* Jean-François Alcover, Aug 10 2018 *)
  • PARI
    N = 15; G = 5; gmax(n) = min(n\2, G);
Q = matrix(N + 1, N + 1);
Qget(n, g) = { if (g < 0 || g > n/2, 0, Q[n+1, g+1]) };
Qset(n, g, v) = { Q[n+1, g+1] = v };
Quadric({x=1}) = {
  Qset(0, 0, x);
  for (n = 1, length(Q)-1, for (g = 0, gmax(n),
    my(t1 = (1+x)*(2*n-1)/3 * Qget(n-1, g),
       t2 = (2*n-3)*(2*n-2)*(2*n-1)/12 * Qget(n-2, g-1),
       t3 = 1/2 * sum(k = 1, n-1, sum(i = 0, g,
       (2*k-1) * (2*(n-k)-1) * Qget(k-1, i) * Qget(n-k-1, g-i))));
    Qset(n, g, (t1 + t2 + t3) * 6/(n+1))));
};
Quadric('x);
concat(apply(p->Vecrev(p/'x), vector(N+1 - 2*G, n, Qget(n-1 + 2*G, G))))

A288288 a(n) is the number of rooted maps with n edges and 8 faces on an orientable surface of genus 5.

Original entry on oeis.org

233454817237201560, 35801820369640556595, 2677324515710001081372, 131989618396827099239715, 4869474711666664850333856, 144282707675416905279319800, 3591928999997575304490876960, 77515666515764938993111323048, 1483610943246601143976044602400, 25624962301264473700614835484334, 404881818003827869935873694190904, 5916336815178383154031082792690874
Offset: 17

Views

Author

Gheorghe Coserea, Jun 11 2017

Keywords

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, this sequence, A288289 f=9, A288290 f=10.
Column 8 of A269925.
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, 5];
Table[a[n], {n, 17, 28}] (* Jean-François Alcover, Oct 17 2018 *)

A288290 a(n) is the number of rooted maps with n edges and 10 faces on an orientable surface of genus 5.

Original entry on oeis.org

28449551653853229900, 5131008990500486096250, 447964809766718459342400, 25606868770179512447281320, 1088463806617771584122226336, 36940703720927769833985462240, 1047632171592441142843472246400, 25624962301264473700614835484334, 553279524558089394499396612588296, 10733417717473916970871163704143300, 189705897479950023040270728219928512
Offset: 19

Views

Author

Gheorghe Coserea, Jun 11 2017

Keywords

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, this sequence.
Column 10 of A269925.
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) ((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, 5];
Table[a[n], {n, 19, 29}] (* Jean-François Alcover, Oct 17 2018 *)

A288281 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 5.

Original entry on oeis.org

59520825, 4304016990, 158959754226, 4034735959800, 79553497760100, 1302772718028600, 18475997006212200, 233454817237201560, 2682208751185413450, 28449551653853229900, 281858111998039476900, 2632472852850938916000, 23350616705746908461520, 197910970615681824664800, 1610886016462484019585600
Offset: 10

Views

Author

Gheorghe Coserea, Jun 09 2017

Keywords

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: this sequence, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
Column 1 of A269925.
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) ((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, 1, 5];
Table[a[n], {n, 10, 24}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: -88179*y*(y-1)^10*(675*y^8 + 9660*y^7 + 19104*y^6 - 38620*y^5 - 26606*y^4 + 51308*y^3 - 10784*y^2 - 5416*y + 1354)/(y-2)^29, where y=A000108(x).

A288282 a(n) is the number of rooted maps with n edges and 2 faces on an orientable surface of genus 5.

Original entry on oeis.org

4304016990, 354949166565, 14805457339920, 420797306522502, 9220982517965400, 166713517116449940, 2595050050431235488, 35801820369640556595, 447016944351510642564, 5131008990500486096250, 54801783386722932356160, 549865627271249187555384, 5223273162178751507973600
Offset: 11

Views

Author

Gheorghe Coserea, Jun 09 2017

Keywords

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, this sequence, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
Column 2 of A269925.
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) ((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, 2, 5];
Table[a[n], {n, 11, 23}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: 3*y*(y-1)^11*(19840275*y^10 + 3054079665*y^9 + 39932223996*y^8 + 81871857210*y^7 - 177595619343*y^6 - 160148276767*y^5 + 319799274321*y^4 - 57293265711*y^3 - 75145589046*y^2 + 28452476366*y - 1512328636)/(y-2)^32, where y=A000108(x).

A288283 a(n) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus 5.

Original entry on oeis.org

158959754226, 14805457339920, 691650582088536, 21853758736216200, 528887751025584600, 10499075716384241952, 178505550201444784920, 2677324515710001081372, 36188783145801243558900, 447964809766718459342400, 5141788096308757330278816, 55267879542927003057175200, 560775739552815581754138816
Offset: 12

Views

Author

Gheorghe Coserea, Jun 09 2017

Keywords

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, this sequence, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
Column 3 of A269925.
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) ((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, 3, 5];
Table[a[n], {n, 12, 24}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: -6*y*(y-1)^12*(1434672330*y^11 + 125297167569*y^10 + 1520299523980*y^9 + 3143130463894*y^8 - 7464422123238*y^7 - 7957464673806*y^6 + 16850577489362*y^5 - 2273292547090*y^4 - 6843677356968*y^3 + 3164962758706*y^2 - 181381616688*y - 58970465680)/(y-2)^35, where y=A000108(x).

A288284 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 5.

Original entry on oeis.org

4034735959800, 420797306522502, 21853758736216200, 762684674663536626, 20269771718252599536, 439591872915483185214, 8127109896970086044280, 131989618396827099239715, 1924446945220467632598816, 25606868770179512447281320, 314937862113457568812798944, 3616708980976267213715063568, 39101467996466899068672052800, 400687469703530771051452630260, 3913896712273232414650041609360
Offset: 13

Views

Author

Gheorghe Coserea, Jun 11 2017

Keywords

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, this sequence, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
Column 4 of A269925.
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) ((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, 4, 5];
Table[a[n], {n, 13, 27}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: 3*y*(y-1)^13*(224289558339*y^12 + 14578605290775*y^11 + 166145326384017*y^10 + 340348495329013*y^9 - 895516337370275*y^8 - 1061973836040211*y^7 + 2408646239898087*y^6 - 205280701572677*y^5 - 1466543072083650*y^4 + 763547357880930*y^3 - 17564852805804*y^2 - 51665824966088*y + 6399222484144)/(y-2)^38, where y=A000108(x).

A288285 a(n) is the number of rooted maps with n edges and 5 faces on an orientable surface of genus 5.

Original entry on oeis.org

79553497760100, 9220982517965400, 528887751025584600, 20269771718252599536, 588564117958709029644, 13881153040572190501512, 277921666244135490925320, 4869474711666664850333856, 76330117260895762678976496, 1088463806617771584122226336, 14304840156674599302991391808, 175067544404400195382759080000
Offset: 14

Views

Author

Gheorghe Coserea, Jun 11 2017

Keywords

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, A288284 f=4, this sequence, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
Column 5 of A269925.
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) ((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, 5, 5];
Table[a[n], {n, 14, 25}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: -12*y*(y-1)^14*(3140032216620*y^13 + 168745438117215*y^12 + 1823095410398560*y^11 + 3655757687054272*y^10 - 10735527168335100*y^9 - 13611993085165141*y^8 + 33238393245141476*y^7 - 1171322344070974*y^6 - 27716201280764020*y^5 + 15575605858027959*y^4 + 683444198956148*y^3 - 2374578542797076*y^2 + 479239083620192*y - 11169074253456)/(y-2)^41, where y=A000108(x).

A288286 a(n) is the number of rooted maps with n edges and 6 faces on an orientable surface of genus 5.

Original entry on oeis.org

1302772718028600, 166713517116449940, 10499075716384241952, 439591872915483185214, 13881153040572190501512, 354556747218700475500140, 7658941714130456546009472, 144282707675416905279319800, 2424036981927621898592714592, 36940703720927769833985462240, 517437278627390310406722691200, 6732676056022023909877001111172
Offset: 15

Views

Author

Gheorghe Coserea, Jun 11 2017

Keywords

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, this sequence, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
Column 6 of A269925.
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) ((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, 6, 5];
Table[a[n], {n, 15, 26}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: 6*y*(y-1)^15*(282058698442290*y^14 + 13234659536432670*y^13 + 136523077378811396*y^12 + 265550247537056832*y^11 - 874424418903920099*y^10 - 1153574344496487459*y^9 + 3042269761791051489*y^8 + 35790516591815337*y^7 - 3265706341059162918*y^6 + 1932218163137003742*y^5 + 268611134157501684*y^4 - 531163056525180208*y^3 + 133718607048292896*y^2 - 1351891439085440*y - 1761044666234112)/(y-2)^44, where y=A000108(x).

A288287 a(n) is the number of rooted maps with n edges and 7 faces on an orientable surface of genus 5.

Original entry on oeis.org

18475997006212200, 2595050050431235488, 178505550201444784920, 8127109896970086044280, 277921666244135490925320, 7658941714130456546009472, 177889367903895880526289600, 3591928999997575304490876960, 64495258714680679471831890624, 1047632171592441142843472246400, 15602830991918991492377865030768, 215367527001361085125596104693328
Offset: 16

Views

Author

Gheorghe Coserea, Jun 11 2017

Keywords

Links

Crossrefs

Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, this sequence, A288288 f=8, A288289 f=9, A288290 f=10.
Column 7 of A269925.
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) ((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, 7, 5];
Table[a[n], {n, 16, 27}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: -24*y*(y-1)^16*(2698126164350850*y^15 + 114214134208709301*y^14 + 1131272022789923528*y^13 + 2118653911175445143*y^12 - 7848128857296958637*y^11 - 10563945755997793403*y^10 + 30156692271220941375*y^9 + 1622522506032620085*y^8 - 39857153689058183268*y^7 + 24443452645454378385*y^6 + 6323328397994465472*y^5 - 10624874505421887856*y^4 + 2992426035154937504*y^3 + 122439286239701680*y^2 - 144788767567212992*y + 11962072115155008)/(y-2)^47, where y=A000108(x).
Showing 1-10 of 10 results.

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