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 1-4 of 4 results.

A241551 Number of partitions p of n such that (number of numbers of the form 5k + 2 in p) is a part of p.

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 16, 25, 34, 49, 66, 90, 119, 161, 211, 279, 357, 465, 595, 764, 968, 1224, 1536, 1933, 2406, 2999, 3703, 4577, 5628, 6910, 8441, 10295, 12507, 15184, 18356, 22163, 26661, 32035, 38395, 45937, 54821, 65321, 77655, 92209, 109242
Offset: 0

Views

Author

Clark Kimberling, Apr 26 2014

Keywords

Comments

Each number in p is counted once, regardless of its multiplicity.

Examples

			a(6) counts these 3 partitions:  321, 2211, 21111.

Crossrefs

Cf. A241549, A241550, A241552, A241553.

Programs

  • Mathematica
    z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]
Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}]  (* A241549 *)
Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}]  (* A241550 *)
Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}]  (* A241551 *)
Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}]  (* A241552 *)
Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}]  (* A241553 *)

A241549 Number of partitions p of n such that (number of numbers of the form 5k in p) is a part of p.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 12, 17, 25, 35, 48, 67, 91, 122, 163, 215, 283, 369, 478, 615, 786, 1004, 1270, 1604, 2014, 2521, 3139, 3902, 4824, 5954, 7314, 8970, 10957, 13362, 16232, 19691, 23804, 28737, 34581, 41559, 49802, 59596, 71139, 84799
Offset: 0

Views

Author

Clark Kimberling, Apr 26 2014

Keywords

Comments

Each number in p is counted once, regardless of its multiplicity.

Examples

			a(6) counts this single partition:  51.

Crossrefs

Cf. A241550, A241551, A241552, A241553.

Programs

  • Mathematica
    z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]
Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}]  (* A241549 *)
Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}]  (* A241550 *)
Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}]  (* A241551 *)
Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}]  (* A241552 *)
Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}]  (* A241553 *)

A241552 Number of partitions p of n such that (number of numbers of the form 5k + 3 in p) is a part of p.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 12, 17, 23, 34, 47, 64, 87, 115, 154, 204, 266, 346, 444, 573, 731, 933, 1174, 1479, 1855, 2320, 2884, 3578, 4411, 5443, 6678, 8185, 9977, 12157, 14753, 17886, 21608, 26058, 31326, 37631, 45066, 53911, 64300, 76609, 91061
Offset: 0

Views

Author

Clark Kimberling, Apr 26 2014

Keywords

Comments

Each number in p is counted once, regardless of its multiplicity.

Examples

			a(6) counts these 2 partitions:  321, 3111.

Crossrefs

Cf. A241549, A241550, A241551, A241553.

Programs

  • Mathematica
    z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]
Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}]  (* A241549 *)
Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}]  (* A241550 *)
Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}]  (* A241551 *)
Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}]  (* A241552 *)
Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}]  (* A241553 *)

A241553 Number of partitions p of n such that (number of numbers of the form 5k + 4 in p) is a part of p.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 12, 17, 25, 33, 49, 65, 90, 119, 159, 210, 277, 358, 466, 593, 766, 968, 1231, 1548, 1942, 2427, 3026, 3747, 4642, 5704, 7022, 8587, 10498, 12775, 15519, 18799, 22730, 27394, 32981, 39558, 47426, 56676, 67650, 80564, 95781
Offset: 0

Views

Author

Clark Kimberling, Apr 26 2014

Keywords

Comments

Each number in p is counted once, regardless of its multiplicity.

Examples

			a(6) counts this single partition:  411.

Crossrefs

Cf. A241549, A241550, A241551, A241552.

Programs

  • Mathematica
    z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]
Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}]  (* A241549 *)
Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}]  (* A241550 *)
Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}]  (* A241551 *)
Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}]  (* A241552 *)
Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}]  (* A241553 *)
Showing 1-4 of 4 results.

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