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 1-3 of 3 results.

A068907 Number of partitions of n modulo 3.

Original entry on oeis.org

1, 1, 2, 0, 2, 1, 2, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 2, 0, 1, 1, 0, 2, 0, 2, 1, 0, 0, 0, 1, 1, 2, 0, 2, 1, 2, 0, 1, 0, 1, 2, 2, 2, 0, 2, 0, 0, 1, 1, 2, 0, 2, 1, 2, 2, 0, 1, 1, 2, 2, 2, 1, 2, 0, 1, 2, 1, 2, 2, 2, 1, 2, 0, 1, 1, 1, 2, 0, 2, 0
Offset: 0

Views

Author

Henry Bottomley, Mar 05 2002

Keywords

Comments

Of the partitions of numbers from 1 to 100000: 33344 are 0, 33193 are 1 and 33463 are 2 modulo 3.

Links

Crossrefs

Cf. A040051, A068908, A068909, A020919.

Programs

Formula

a(n) = A010872(A000041(n)) = A068906(3, n)
a(n) = Pm(n,1) with Pm(n,k) = if kReinhard Zumkeller, Jun 09 2009

A068908 Number of partitions of n modulo 5.

Original entry on oeis.org

1, 1, 2, 3, 0, 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 1, 2, 0, 0, 2, 2, 2, 0, 0, 3, 1, 0, 3, 0, 4, 2, 4, 3, 0, 3, 2, 2, 0, 0, 3, 3, 4, 1, 0, 4, 3, 4, 3, 0, 1, 3, 4, 1, 0, 1, 3, 4, 0, 0, 2, 0, 1, 4, 0, 3, 0, 4, 0, 0, 3, 0, 3, 4, 0, 4, 1, 3, 4, 0, 1, 2, 0, 4, 0, 2, 2, 3, 4, 0, 3, 4, 2, 2, 0, 4, 4, 0, 1, 0, 2, 1, 4, 0, 0
Offset: 0

Views

Author

Henry Bottomley, Mar 05 2002

Keywords

Comments

Of the partitions of numbers from 1 to 100000: 36256 are 0, 15758 are 1, 16133 are 2, 16028 are 3 and 15825 are 4 modulo 5, largely because the number of partitions of 5m+4 is always a multiple of 5.

Links

Crossrefs

Cf. A000041, A010874, A068906.
Cf. A040051, A068907, A068909, A020919.

Programs

  • Mathematica
    Mod[PartitionsP[Range[0,110]],5] (* Harvey P. Dale, Dec 20 2023 *)
  • PARI
    a(n) = numbpart(n) % 5; \\ Michel Marcus, Jul 14 2022

Formula

a(n) = A010874(A000041(n)) = A068906(5, n).
a(n) = Pm(n,1) with Pm(n,k) = if kReinhard Zumkeller, Jun 09 2009]

A068906 Square array read by ascending antidiagonals of partitions of k modulo n.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 1, 1, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 0, 0, 3, 2, 5, 3, 2, 1, 0, 0, 1, 3, 1, 1, 5, 3, 2, 1, 0, 0, 0, 2, 0, 5, 0, 5, 3, 2, 1, 0, 0, 0, 2, 2, 3, 4, 7, 5, 3, 2, 1, 0, 1, 2, 2, 0, 4, 1, 3, 7, 5, 3, 2, 1, 0, 1, 2, 0, 2, 0, 1, 7, 2, 7, 5, 3, 2, 1
Offset: 1

Views

Author

Henry Bottomley, Mar 05 2002

Keywords

Comments

0 is disproportionately common modulo 5, 7 and 11, largely because T(5,5m+4)=T(7,7m+5)=T(11,11m+6)=0.

Examples

			Rows start 0,0,0,0,0,...; 1,0,1,1,1,...; 1,2,0,2,1,...; 1,2,3,1,3,...; 1,2,3,0,2,1,...; 1,2,3,5,1,5,...; 1,2,3,5,0,...; 1,2,3,5,7,...; etc.

Links

Crossrefs

Rows 2, 3, 5, 7 and 11 give A040051, A068907, A068908, A068909, A020919.

Formula

T(n, k) =A051127(n, A000041(k))
Showing 1-3 of 3 results.

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

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