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 }.

A306895 Sum over all partitions of n of the power tower evaluation x^y^...^z, where x, y, ..., z are the parts in (weakly) increasing order.

Original entry on oeis.org

1, 1, 3, 5, 11, 18, 72, 387, 134349386, 115792089237316195423570985008687907853269984665640566457309223244801371506483
Offset: 0

Views

Author

Alois P. Heinz, Mar 15 2019

Keywords

Comments

a(10) has 40403562 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 + 1^1^1^1^2 + 1^1^2^2 + 2^2^2 + 1^1^1^3 + 1^2^3 + 3^3 + 1^1^4 + 2^4 + 1^5 + 6 = 1 + 1 + 1 + 16 + 1 + 1 + 27 + 1 + 16 + 1 + 6 = 72.

Links

Crossrefs

Cf. A006906, A066186, A306884, A306901, A306902, A306903, A306919.

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);

A306918 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 decreasing order.

Original entry on oeis.org

1, 1, 2, 5, 7, 18, 36, 118, 265, 263212, 2217881, 152599933940, 542101086242752217003726400434973829461152534, 63340828764059520458379290673240751904836319648345
Offset: 0

Views

Author

Alois P. Heinz, Mar 16 2019

Keywords

Comments

a(14) = 620606987...270037949 has 183231 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) = 3^2^1 + 4^2 + 5^1 + 6 = 9 + 16 + 5 + 6 = 36.

Links

Crossrefs

Cf. A022629, A066189, A306884, A306919.

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..13);
  • 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, ReverseSort /@ Select[IntegerPartitions[n], Length@# == Length@ Union@# &]}];
a /@ Range[0, 13] (* Jean-François Alcover, May 04 2020, after Maple *)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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