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 1-6 of 6 results.

A248730 Number of partitions of 5^n.

Original entry on oeis.org

1, 7, 1958, 3163127352, 1606903190858354689128371, 8630901377559029573671524821295260243701883575513498104067
Offset: 0

Views

Author

Robert G. Wilson v, Oct 12 2014

Keywords

Comments

Next term is too big to be included.

Crossrefs

Programs

  • Magma
    [NumberOfPartitions(5^n): n in [0..6]]; // Vincenzo Librandi, Oct 13 2014
  • Mathematica
    Table[ PartitionsP[ 5^n], {n, 0, 6}]
  • PARI
    vector(8, n, n--; numbpart(5^n)) \\ Michel Marcus, Oct 13 2014
    

A248732 Number of partitions of 6^n.

Original entry on oeis.org

1, 11, 17977, 15285151248481, 1398703012615213588677365804960180341, 3173477897288016617984809197028065610087051214582584606785402878333070481745149246796102615681
Offset: 0

Views

Author

Robert G. Wilson v, Oct 12 2014

Keywords

Crossrefs

Programs

  • Magma
    [NumberOfPartitions(6^n): n in [0..6]]; // Vincenzo Librandi, Oct 13 2014
  • Mathematica
    Table[ PartitionsP[ 6^n], {n, 0, 5}]

Formula

A248732 = A000041 o A000400. \\ M. F. Hasler, Oct 16 2014

A248729 Number of digits in the decimal expansion of the number of partitions of 3^n.

Original entry on oeis.org

1, 1, 2, 4, 8, 15, 27, 48, 86, 152, 266, 463, 806, 1400, 2429, 4212, 7301, 12651, 21918, 37969, 65771, 113926, 197332, 341797, 592018, 1025414, 1776077
Offset: 0

Views

Author

Robert G. Wilson v, Oct 12 2014

Keywords

Crossrefs

Programs

  • Magma
    [Floor(Log(10,(NumberOfPartitions(3^n))))+1: n in [0..12]]; // Vincenzo Librandi, Oct 13 2014
  • Mathematica
    f[n_] := Floor[ Log[10, PartitionsP[ 3^n]] + 1]; Table[ f@n, {n, 0, 30}]
    IntegerLength[PartitionsP[3^Range[0,30]]] (* Harvey P. Dale, Sep 05 2023 *)
  • PARI
    a(n) = #Str(numbpart(3^n)); \\ Michel Marcus, Oct 13 2014
    

Formula

a(n) = A055642(A248728(n)). - R. J. Mathar, Nov 17 2014

A248734 Number of partitions of 7^n.

Original entry on oeis.org

1, 15, 173525, 175943559810422753, 229866006383458830949778967121025947053151071434926
Offset: 0

Views

Author

Robert G. Wilson v, Oct 12 2014

Keywords

Comments

Next term is too big to be included.

Crossrefs

Programs

  • Magma
    [NumberOfPartitions(7^n): n in [0..6]]; // Vincenzo Librandi, Oct 13 2014
    
  • Mathematica
    Table[ PartitionsP[ 7^n], {n, 0, 5}]
  • PARI
    a(n) = numbpart(7^n) \\ Michel Marcus, Oct 18 2014

Formula

a(n) = A000041(7^n). - Michel Marcus, Oct 18 2014

A347615 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) is the number of partitions of n^k.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 3, 1, 1, 1, 22, 30, 5, 1, 1, 1, 231, 3010, 231, 7, 1, 1, 1, 8349, 18004327, 1741630, 1958, 11, 1, 1, 1, 1741630, 133978259344888, 365749566870782, 3163127352, 17977, 15, 1, 1, 1, 4351078600, 233202632378520643600875145, 61847822068260244309086870983975, 1606903190858354689128371, 15285151248481, 173525, 22, 1
Offset: 0

Views

Author

Seiichi Manyama, Sep 08 2021

Keywords

Examples

			Square array begins:
  1, 1,   1,       1,               1, ...
  1, 1,   1,       1,               1, ...
  1, 2,   5,      22,             231, ...
  1, 3,  30,    3010,        18004327, ...
  1, 5, 231, 1741630, 365749566870782, ...
		

Crossrefs

Columns k=0..3 give A000012, A000041, A072213, A128854.
Rows n=0+1, 2-10 give A000012, A068413, A248728, A068413(2*n), A248730, A248732, A248734, A068413(3*n), A248728(2*n), A070177.
Main diagonal gives A347607.

Programs

  • PARI
    T(n, k) = numbpart(n^k);

Formula

T(n,k) = A000041(n^k).

A070235 Number of partitions of 3^n into distinct terms.

Original entry on oeis.org

1, 2, 8, 192, 84756, 5807301632, 2496696209705056142, 4077067982967062771640042697374910, 1661834856564765736512658856496529945178404778001420955780288
Offset: 0

Views

Author

Robert G. Wilson v, May 08 2002

Keywords

Crossrefs

Programs

  • Mathematica
    Table[ PartitionsQ[3^n], {n, 0, 10}]

Formula

a(n) ~ exp(Pi*sqrt(3^(n-1)))/(4*3^(3*n/4+1/4)). - Ilya Gutkovskiy, Jan 13 2017
Showing 1-6 of 6 results.