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 1-5 of 5 results.

A215266 Number of solid standard Young tableaux of cylindrical shape lambda X 2, where lambda ranges over all partitions of n.

Original entry on oeis.org

1, 1, 4, 26, 258, 3346, 54108, 1054256, 24161966, 634230122, 18806776982, 622011916184, 22754818956246, 912075762692584, 39755634279964662, 1872279469323840472, 94783193260373606758, 5135585509536795416348, 296656123838796109849526, 18200829821539972354967252
Offset: 0

Views

Author

Alois P. Heinz, Aug 07 2012

Keywords

Links

Crossrefs

Column k=2 of A215204.

Programs

  • Maple
    b:= proc(l) option remember; local m; m:= nops(l);
      `if`({map(x-> x[], l)[]}minus{0}={}, 1, add(add(`if`(l[i][j]>
      `if`(i=m or nops(l[i+1])
      `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
       j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
    end:
g:= proc(n, i, l) `if`(n=0 or i=1, b(map(x->[2$x], [l[], 1$n])),
       add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))
    end:
a:= n-> g(n, n, []):
seq(a(n), n=0..12);

A290202 Number of solid standard Young tableaux of cylindrical shape lambda X 3, where lambda ranges over all partitions of n.

Original entry on oeis.org

1, 1, 10, 276, 14318, 1214358, 150910592, 25454753376, 5599142988564, 1557618719594808, 532482249378122738, 218108013886160729600, 105215894641522373026220, 59025152558043462549357094, 38095446968224172036448488814, 27985301641485576224718954999962
Offset: 0

Views

Author

Alois P. Heinz, Jul 23 2017

Keywords

Links

Crossrefs

Column k=3 of A215204.

Programs

  • Maple
    b:= proc(l) option remember; local m; m:= nops(l);
      `if`({map(x-> x[], l)[]}minus{0}={}, 1, add(add(`if`(l[i][j]>
      `if`(i=m or nops(l[i+1])
      `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
       j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
    end:
g:= proc(n, i, l) `if`(n=0 or i=1, b(map(x->[3$x], [l[], 1$n])),
       add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))
    end:
a:= n-> g(n$2, []):
seq(a(n), n=0..10);
  • Mathematica
    b[l_] := b[l] = With[{m = Length[l]}, If[Union[l // Flatten] ~Complement~ {0} == {}, 1, Sum[Sum[If[l[[i, j]] > If[i == m || Length[l[[i + 1]]] < j, 0, l[[i + 1, j]]] && l[[i, j]] > If[Length[l[[i]]] == j, 0, l[[i, j + 1]]], b[ReplacePart[l, i -> ReplacePart[l[[i]], j -> l[[i, j]] - 1]]], 0], {j, 1, Length[l[[i]]]}], {i, 1, m}]]];
g[n_, i_, k_, l_] := If[n == 0 || i == 1, b[Table[k, {#}]& /@ Join[l, Table[1, {n}]]], Sum[g[n - i*j, i - 1, k, Join[l, Table[i, {j}]]], {j, 0, n/i}]];
a[n_] := g[n, n, 3, {}]; Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Dec 28 2022, after Alois P. Heinz in A215204 *)

A290214 Number of solid standard Young tableaux of cylindrical shape lambda X 4, where lambda ranges over all partitions of n.

Original entry on oeis.org

1, 1, 28, 3740, 1161678, 741215012, 840790914296, 1439884504332480, 3576753835657635164, 12524266750764601753576, 59517682037036901339560926, 363169855509323114958694015304, 2774932810808589820997792848479674, 26216044235174202943266623056680424524
Offset: 0

Views

Author

Alois P. Heinz, Jul 24 2017

Keywords

Links

Crossrefs

Column k=4 of A215204.

Programs

  • Maple
    b:= proc(l) option remember; local m; m:= nops(l);
      `if`({map(x-> x[], l)[]}minus{0}={}, 1, add(add(`if`(l[i][j]>
      `if`(i=m or nops(l[i+1])
      `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
       j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
    end:
g:= proc(n, i, l) `if`(n=0 or i=1, b(map(x->[4$x], [l[], 1$n])),
       add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))
    end:
a:= n-> g(n$2, []):
seq(a(n), n=0..8);
  • Mathematica
    b[l_] := b[l] = With[{m = Length[l]}, If[Union[l // Flatten] ~Complement~ {0} == {}, 1, Sum[Sum[If[l[[i, j]] > If[i == m || Length[l[[i + 1]]] < j, 0, l[[i + 1, j]]] && l[[i, j]] > If[Length[l[[i]]] == j, 0, l[[i, j + 1]]], b[ReplacePart[l, i -> ReplacePart[l[[i]], j -> l[[i, j]] - 1]]], 0], {j, 1, Length[l[[i]]]}], {i, 1, m}]]];
g[n_, i_, k_, l_] := If[n == 0 || i == 1, b[Table[k, {#}] & /@ Join[l, Table[1, {n}]]], Sum[g[n - i*j, i - 1, k, Join[l, Table[i, {j}]]], {j, 0, n/i}]];
a[n_] := g[n, n, 4, {}];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Dec 28 2022, after Alois P. Heinz in A215204 *)

A290225 Number of solid standard Young tableaux of cylindrical shape lambda X n, where lambda ranges over all partitions of n.

Original entry on oeis.org

1, 1, 4, 276, 1161678, 620383261034, 80434777704834144228, 3212151962391797592956111856142, 58141033434729590882944205957642581926272684, 738506234630963222745737660670442498620046849638365979249010
Offset: 0

Views

Author

Alois P. Heinz, Jul 24 2017

Keywords

Links

Crossrefs

Main diagonal of A215204.

Programs

  • Maple
    b:= proc(l) option remember; local m; m:= nops(l);
      `if`({map(x-> x[], l)[]}minus{0}={}, 1, add(add(`if`(l[i][j]>
      `if`(i=m or nops(l[i+1])
      `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
       j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
    end:
g:= proc(n, i, k, l) `if`(n=0 or i=1, b(map(x-> [k$x], [l[], 1$n])),
       add(g(n-i*j, i-1, k, [l[], i$j]), j=0..n/i))
    end:
a:= n-> g(n$3, []):
seq(a(n), n=0..6);
  • Mathematica
    b[l_] := b[l] = With[{m = Length[l]}, If[Union[l // Flatten] ~Complement~ {0} == {}, 1, Sum[Sum[If[l[[i, j]] > If[i == m || Length[l[[i + 1]]] < j, 0, l[[i + 1, j]]] && l[[i, j]] > If[Length[l[[i]]] == j, 0, l[[i, j + 1]]], b[ReplacePart[l, i -> ReplacePart[l[[i]], j -> l[[i, j]] - 1]]], 0], {j, 1, Length[l[[i]]]}], {i, 1, m}]]];
g[n_, i_, k_, l_] := If[n == 0 || i == 1, b[Table[k, {#}] & /@ Join[l, Table[1, {n}]]], Sum[g[n - i*j, i - 1, k, Join[l, Table[i, {j}]]], {j, 0, n/i}]];
a[n_] := g[n, n, n, {}];
Table[a[n], {n, 0, 7}] (* Jean-François Alcover, Dec 28 2022, after Alois P. Heinz in A215204 *)

Formula

a(n) = A215204(n,n).

A290274 Number of solid standard Young tableaux of cylindrical shape lambda X 5, where lambda ranges over all partitions of n.

Original entry on oeis.org

1, 1, 84, 58604, 118316062, 620383261034, 7137345113624878, 136938419662960675110, 4248619239382421064760418, 208764720295510001353706916224, 15549729565895424021059338656785142, 1588531886834159978895386134546068562294, 215569983507625108792605406075783194767331496
Offset: 0

Views

Author

Alois P. Heinz, Jul 25 2017

Keywords

Links

Crossrefs

Column k=5 of A215204.

Programs

  • Maple
    b:= proc(l) option remember; local m; m:= nops(l);
      `if`({map(x-> x[], l)[]}minus{0}={}, 1, add(add(`if`(l[i][j]>
      `if`(i=m or nops(l[i+1])
      `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
       j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
    end:
g:= proc(n, i, l) `if`(n=0 or i=1, b(map(x->[5$x], [l[], 1$n])),
       add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))
    end:
a:= n-> g(n$2, []):
seq(a(n), n=0..8);
  • Mathematica
    b[l_] := b[l] = With[{m = Length[l]}, If[Union[l // Flatten] ~Complement~ {0} == {}, 1, Sum[Sum[If[l[[i, j]] > If[i == m || Length[l[[i + 1]]] < j, 0, l[[i + 1, j]]] && l[[i, j]] > If[Length[l[[i]]] == j, 0, l[[i, j + 1]]], b[ReplacePart[l, i -> ReplacePart[l[[i]], j -> l[[i, j]] - 1]]], 0], {j, 1, Length[l[[i]]]}], {i, 1, m}]]];
g[n_, i_, k_, l_] := If[n == 0 || i == 1, b[Table[k, {#}] & /@ Join[l, Table[1, {n}]]], Sum[g[n - i*j, i - 1, k, Join[l, Table[i, {j}]]], {j, 0, n/i}]];
a[n_] := g[n, n, 5, {}];
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Dec 28 2022, after Alois P. Heinz in A215204 *)
Showing 1-5 of 5 results.

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