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.

Previous Showing 11-14 of 14 results.

A238780 Number of palindromic partitions of n whose greatest part has multiplicity 4.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 2, 5, 4, 7, 5, 10, 8, 14, 11, 20, 16, 26, 21, 37, 31, 48, 40, 65, 55, 85, 72, 113, 97, 145, 125, 190, 165, 242, 211, 313, 274, 396, 348, 505, 446, 633, 561, 801, 713, 998, 890, 1249, 1118, 1548, 1389, 1922, 1730
Offset: 0

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(8) counts these partitions (written as palindromes):  3333, 11222211.

Crossrefs

Cf. A025065, A087897, A238779.

Programs

  • Mathematica
    z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Max[#]] == k) &]
Table[p[n, 1], {n, 1, 12}]
t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A000009(n-1), n>=1 *)
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238779 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A087897(n-3), n>=3 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238780 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238791 Number of palindromic partitions of n such that the multiplicities of the least and greatest parts are equal.

Original entry on oeis.org

1, 2, 2, 3, 2, 5, 2, 5, 3, 7, 2, 11, 3, 10, 6, 15, 5, 22, 7, 28, 12, 33, 15, 52, 21, 59, 33, 84, 38, 112, 56, 145, 77, 178, 103, 251, 132, 300, 184, 404, 229, 507, 304, 645, 398, 800, 506, 1040, 639, 1270, 832, 1608, 1032, 1988, 1310, 2479, 1640, 3031, 2053
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(10) counts these 7 partitions (written as palindromes): [10], [5,5], [1,4,4,1], [2,3,3,2], [1,3,2,3,1], [2,2,2,2,2], [1,1,1,1,1,1,1,1,1,1].

Crossrefs

Cf. A025065, A238792, A238793, A238779.

Programs

  • Mathematica
    z = 40; p[n_] := p[n] = Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] == Count[#, Max[#]]) &]; Table[p[n], {n, 1, 12}]
Table[Length[p[n]], {n, 1, z}]

A238792 Number of palindromic partitions of n such that (multiplicity of least part) = 2*(multiplicity of greatest part).

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 2, 3, 3, 5, 4, 8, 7, 12, 11, 17, 14, 24, 22, 34, 31, 47, 39, 66, 56, 85, 76, 115, 98, 158, 130, 198, 176, 260, 226, 342, 289, 432, 382, 558, 476, 716, 611, 895, 784, 1129, 975, 1430, 1229, 1775, 1551, 2211, 1914, 2756, 2385, 3394, 2964
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(10) counts these 5 partitions (written as palindromes):  181, 262, 343, 12421, 113311.

Crossrefs

Cf. A025065, A238791, A238793, A238779.

Programs

  • Mathematica
    z = 40; p[n_] := p[n] = Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] == 2*Count[#, Max[#]]) &]; Table[p[n], {n, 1, 12}]
Table[Length[p[n]], {n, 1, z}]

A238793 Number of palindromic partitions of n such that 2*(multiplicity of least part) = (multiplicity of greatest part).

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 3, 1, 3, 3, 6, 5, 6, 5, 9, 9, 13, 10, 17, 13, 23, 18, 29, 23, 37, 32, 48, 37, 64, 48, 81, 60, 99, 77, 130, 94, 158, 123, 200, 145, 252, 182, 309, 224, 381, 277, 475, 331, 575, 414, 712, 497, 866, 605, 1049, 736, 1274, 883, 1555
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(15) counts these 6 partitions (written as palindromes):  717, 636, 25152, 13431, 12233221..

Crossrefs

Cf. A025065, A238791, A238792, A238779.

Programs

  • Mathematica
    z = 65; p[n_] := p[n] = Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (2*Count[#, Min[#]] == Count[#, Max[#]]) &]; Table[p[n], {n, 1, 16}]
t1 = Table[Length[p[n]], {n, 1, z}]
(* Peter J. C. Moses, Mar 03 2014 *)
Previous Showing 11-14 of 14 results.

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