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 1-10 of 14 results. Next

A238781 Number of palindromic partitions of n whose least part has multiplicity 1.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 2, 6, 4, 6, 4, 10, 5, 12, 7, 16, 8, 20, 10, 27, 14, 32, 16, 44, 19, 53, 25, 69, 31, 84, 36, 108, 47, 130, 55, 167, 67, 202, 83, 252, 99, 305, 119, 380, 146, 456, 173, 564, 208, 676, 250, 826, 298, 991, 352, 1205, 424, 1435
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(11) counts these partitions (written as palindromes):  [11], [5,1,5], [4,3,4], [2,3,1,3,2].

Crossrefs

Cf. A025065, A238782, A238783, A238784, A238779.

Programs

  • Mathematica
    z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] == k) &]
Table[p[n, 1], {n, 1, 12}]
t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A238781 *)
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238782 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238783 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238784 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238782 Number of palindromic partitions of n whose least part has multiplicity 2.

Original entry on oeis.org

0, 1, 0, 2, 1, 3, 2, 5, 3, 9, 5, 11, 9, 18, 12, 25, 18, 35, 26, 48, 36, 67, 50, 87, 69, 119, 91, 157, 123, 206, 162, 266, 213, 349, 277, 443, 360, 572, 460, 725, 590, 919, 750, 1156, 950, 1456, 1195, 1812, 1502, 2263, 1872, 2802, 2334, 3468, 2892, 4267, 3574
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(8) counts these partitions (written as palindromes):  161, 44, 422, 1331, 12221.

Crossrefs

Cf. A025065, A238781, A238783, A238784, A238779.

Programs

  • Mathematica
    z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] == k) &]
Table[p[n, 1], {n, 1, 12}]
t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A238781 *)
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238782 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238783 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238784 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238783 Number of palindromic partitions of n whose least part has multiplicity 3.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 1, 5, 1, 5, 3, 8, 2, 10, 4, 13, 6, 16, 6, 25, 7, 28, 11, 38, 13, 48, 16, 61, 22, 75, 25, 100, 30, 119, 41, 153, 47, 186, 59, 234, 73, 283, 87, 356, 106, 426, 132, 528, 154, 639, 186, 781, 227, 935, 271, 1143, 322, 1362
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(9) counts these partitions (written as palindromes):  333, 31113.

Crossrefs

Cf. A025065, A238781, A238782, A238784, A238779.

Programs

  • Mathematica
    z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] == k) &]
Table[p[n, 1], {n, 1, 12}]
t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A238781 *)
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238782 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238783 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238784 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238784 Number of palindromic partitions of n whose least part has multiplicity 4.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 1, 3, 1, 3, 3, 7, 4, 9, 6, 15, 10, 19, 15, 30, 21, 39, 30, 56, 41, 75, 58, 103, 77, 132, 106, 181, 139, 231, 185, 307, 241, 392, 314, 508, 406, 643, 523, 826, 665, 1037, 849, 1313, 1070, 1638, 1350, 2057, 1689, 2547, 2112, 3172, 2622, 3902
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(12) counts these 7 partitions (written as palindromes):  11811, 114411, 22422, 1124211, 3333, 1132311, 11222211.

Crossrefs

Cf. A025065, A238781, A238782, A238783, A238779.

Programs

  • Mathematica
    z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] == k) &]
Table[p[n, 1], {n, 1, 12}]
t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A238781 *)
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238782 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238783 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238784 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238785 Number of palindromic partitions of n whose greatest part has multiplicity <= 2.

Original entry on oeis.org

1, 2, 1, 3, 3, 5, 6, 9, 9, 15, 16, 23, 24, 36, 37, 54, 55, 78, 81, 113, 115, 161, 164, 223, 228, 310, 315, 423, 430, 572, 582, 768, 778, 1023, 1037, 1349, 1368, 1772, 1793, 2309, 2336, 2992, 3027, 3856, 3896, 4946, 4996, 6305, 6369, 8012, 8086, 10129, 10220
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(6) counts these partitions (written as palindromes):  6, 141, 33, 1221, 11211.

Crossrefs

Cf. A025065, A238786, A238787, 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}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238785 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238786 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238787 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238786 Number of palindromic partitions of n whose greatest part has multiplicity <= 3.

Original entry on oeis.org

1, 2, 2, 3, 3, 6, 6, 10, 10, 16, 17, 25, 26, 38, 40, 57, 59, 83, 86, 119, 123, 169, 174, 235, 241, 325, 333, 443, 453, 599, 612, 802, 818, 1067, 1087, 1407, 1432, 1845, 1876, 2401, 2440, 3110, 3158, 4003, 4062, 5130, 5202, 6537, 6625, 8298, 8406, 10483
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(8) counts these 10 partitions (written as palindromes):  8, 161, 44, 242, 11411, 323, 1331, 12221, 112211, 1112111.

Crossrefs

Cf. A025065, A238785, A238787, 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}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238785 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238786 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238787 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238787 Number of palindromic partitions of n whose greatest part has multiplicity <= 4.

Original entry on oeis.org

1, 2, 2, 4, 3, 6, 6, 11, 11, 17, 18, 27, 28, 41, 42, 62, 63, 90, 91, 129, 131, 183, 185, 255, 257, 351, 354, 480, 484, 647, 652, 867, 873, 1152, 1159, 1520, 1529, 1990, 2001, 2591, 2605, 3352, 3369, 4316, 4336, 5526, 5550, 7042, 7071, 8931, 8967, 11284
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(8) counts these 11 partitions (written as palindromes):  8, 161, 44, 242, 11411, 323, 1331, 2222, 12221, 112211, 1112111.

Crossrefs

Cf. A025065, A238785, A238786, 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}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238785 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238786 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238787 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238788 Number of palindromic partitions of n whose least part has multiplicity <= 2.

Original entry on oeis.org

1, 2, 1, 3, 3, 4, 4, 7, 6, 11, 9, 13, 15, 22, 18, 29, 28, 40, 38, 55, 52, 75, 70, 97, 96, 133, 123, 173, 167, 225, 215, 291, 282, 380, 361, 479, 468, 619, 590, 780, 757, 986, 952, 1239, 1202, 1555, 1500, 1931, 1882, 2409, 2328, 2975, 2898, 3676, 3568, 4517
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(8) counts these 7 partitions (written as palindromes):  8, 161, 44, 242, 323, 1331, 12221

Crossrefs

Cf. A025065, A238789, A238790, A238779.

Programs

  • Mathematica
    z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] <= k) &]
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}]  (* A238788 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}]  (* A238789 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}]  (* A238790 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238789 Number of palindromic partitions of n whose least part has multiplicity <= 3.

Original entry on oeis.org

1, 2, 2, 3, 3, 5, 5, 7, 8, 11, 11, 15, 17, 23, 23, 30, 33, 43, 46, 57, 62, 79, 83, 103, 112, 139, 148, 180, 195, 236, 253, 304, 330, 396, 422, 501, 543, 644, 690, 810, 876, 1027, 1105, 1286, 1388, 1614, 1734, 2004, 2165, 2496, 2684, 3081, 3324, 3808, 4096
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(9) counts these 8 partitions (written as palindromes):  9, 171, 252, 414, 333, 13131, 12321, 22122.

Crossrefs

Cf. A025065, A238788, A238790, A238779.

Programs

  • Mathematica
    z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] <= k) &]
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}]  (* A238788 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}]  (* A238789 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}]  (* A238790 *)
(* Peter J. C. Moses, Mar 03 2014 *)

A238790 Number of palindromic partitions of n whose least part has multiplicity <= 4.

Original entry on oeis.org

1, 2, 2, 4, 3, 6, 6, 10, 9, 14, 14, 22, 21, 32, 29, 45, 43, 62, 61, 87, 83, 118, 113, 159, 153, 214, 206, 283, 272, 368, 359, 485, 469, 627, 607, 808, 784, 1036, 1004, 1318, 1282, 1670, 1628, 2112, 2053, 2651, 2583, 3317, 3235, 4134, 4034, 5138, 5013, 6355
Offset: 1

Views

Author

Clark Kimberling, Mar 05 2014

Keywords

Comments

Palindromic partitions are defined at A025065.

Examples

			a(8) counts these 10 partitions (written as palindromes):  8, 161, 44, 242, 11411, 323, 1331, 2222, 12221, 112211.

Crossrefs

Cf. A025065, A238788, A238789, A238779.

Programs

  • Mathematica
    z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] <= k) &]
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}]  (* A238788 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}]  (* A238789 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}]  (* A238790 *)
(* Peter J. C. Moses, Mar 03 2014 *)
Showing 1-10 of 14 results. Next

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