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.

A306901 Sum over all partitions of n of the bitwise AND of the parts.

Original entry on oeis.org

0, 1, 3, 4, 8, 9, 14, 13, 24, 28, 36, 38, 55, 54, 68, 75, 106, 120, 154, 168, 208, 228, 269, 298, 374, 404, 475, 530, 618, 682, 808, 896, 1080, 1220, 1410, 1581, 1828, 2022, 2322, 2598, 2963, 3278, 3732, 4128, 4684, 5218, 5888, 6550, 7418, 8192, 9198, 10187
Offset: 0

Views

Author

Alois P. Heinz, Mar 15 2019

Keywords

Links

Crossrefs

Cf. A006906, A066186, A306884, A306895, A306902, A306903, A306923.

Programs

  • Maple
    b:= proc(n, i, r) option remember; `if`(i<1, 0, (t->
      `if`(i b(n$2, 2^ilog2(2*n)-1):
seq(a(n), n=0..55);

A306902 Sum over all partitions of n of the bitwise OR of the parts.

Original entry on oeis.org

0, 1, 3, 7, 13, 23, 40, 67, 103, 156, 231, 340, 486, 689, 964, 1352, 1845, 2507, 3363, 4500, 5937, 7814, 10174, 13247, 17064, 21930, 27957, 35616, 45009, 56805, 71252, 89320, 111282, 138479, 171421, 212021, 260974, 320837, 392753, 480395, 585239, 712163, 863536
Offset: 0

Views

Author

Alois P. Heinz, Mar 15 2019

Keywords

Links

Crossrefs

Cf. A006906, A066186, A306884, A306895, A306901, A306903, A306924.

Programs

  • Maple
    b:= proc(n, i, r) option remember; `if`(i<1, 0, (t->
      `if`(i b(n$2, 0):
seq(a(n), n=0..45);

A306903 Sum over all partitions of n of the bitwise XOR of the parts.

Original entry on oeis.org

0, 1, 2, 7, 8, 19, 26, 61, 70, 126, 146, 270, 308, 519, 604, 1054, 1222, 1929, 2208, 3454, 3930, 5862, 6576, 9833, 11102, 16052, 17904, 25752, 28764, 40479, 44830, 62988, 70188, 97151, 107662, 148141, 164710, 223783, 247380, 334035, 370406, 495313, 547000
Offset: 0

Views

Author

Alois P. Heinz, Mar 15 2019

Keywords

Links

Crossrefs

Cf. A006906, A066186, A067567, A306884, A306895, A306901, A306902, A306925.

Programs

  • Maple
    b:= proc(n, i, r) option remember; `if`(i<1, 0, (t->
      `if`(i b(n$2, 0):
seq(a(n), n=0..45);

Formula

a(n) is odd <=> n in { A067567 }.

A306884 Sum over all partitions of n of the power tower evaluation x^y^...^z, where x, y, ..., z are the parts in (weakly) decreasing order.

Original entry on oeis.org

1, 1, 3, 6, 14, 28, 93, 270, 86170, 7625640881546
Offset: 0

Views

Author

Alois P. Heinz, Mar 15 2019

Keywords

Comments

a(10) = 200352993...611306920 has 19729 decimal digits.

Examples

			a(0) = 1 because the empty partition () has no parts, the exponentiation operator ^ is right-associative, and 1 is the right identity of exponentiation.
a(6) = 1^1^1^1^1^1 + 2^1^1^1^1 + 2^2^1^1 + 2^2^2 + 3^1^1^1 + 3^2^1 + 3^3 + 4^1^1 + 4^2 + 5^1 + 6 = 1 + 2 + 4 + 16 + 3 + 9 + 27 + 4 + 16 + 5 + 6 = 93.

Links

Crossrefs

Cf. A006906, A066186, A306895, A306901, A306902, A306903, A306918.

Programs

  • Maple
    f:= l-> `if`(l=[], 1, l[1]^f(subsop(1=(), l))):
a:= n-> add(f(sort(l, `>`)), l=combinat[partition](n)):
seq(a(n), n=0..9);

A306919 Sum over all partitions of n into distinct parts of the power tower evaluation x^y^...^z, where x, y, ..., z are the parts in increasing order.

Original entry on oeis.org

1, 1, 2, 4, 5, 14, 24, 122, 318, 2417851639229258349414245, 14134776518227074636666380005943348126619871175004951664972849610340964762
Offset: 0

Views

Author

Alois P. Heinz, Mar 16 2019

Keywords

Examples

			a(0) = 1 because the empty partition () has no parts, the exponentiation operator ^ is right-associative, and 1 is the right identity of exponentiation.
a(6) = 1^2^3 + 2^4 + 1^5 + 6 = 1 + 16 + 1 + 6 = 24.

Links

Crossrefs

Cf. A022629, A066189, A306895, A306918.

Programs

  • Maple
    d:= proc(l) local i; for i to nops(l)-1 do
       if l[i]=l[i+1] then return fi od; l
    end:
f:= l-> `if`(l=[], 1, l[1]^f(subsop(1=(), l))):
a:= n-> add(f(l), l=map(l->d(sort(l, `<`)), combinat[partition](n))):
seq(a(n), n=0..11);
  • Mathematica
    d[l_] := Module[{i}, For[i = 1, i <= Length[l]-1 , i++, If[l[[i]] == l[[i+1]], Return[]]]; l];
f[l_] := If[l == {}, 1, l[[1]]^f[Delete[l, 1]]];
a[n_] := Sum[f[l], {l, Sort /@ Select[IntegerPartitions[n], Length@# == Length @ Union@#&]}];
a /@ Range[0, 11] (* Jean-François Alcover, May 03 2020, after Maple *)
Showing 1-5 of 5 results.

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