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 1-5 of 5 results.

A036889 Number of partitions of 5n such that cn(1,5) = cn(4,5) <= cn(0,5) = cn(2,5) = cn(3,5).

Original entry on oeis.org

0, 1, 4, 12, 29, 66, 137, 279, 546, 1057, 2000, 3746, 6886, 12508, 22360, 39477, 68736, 118309, 201207, 338672, 564211, 931342, 1523628, 2472228, 3979651, 6359094, 10088975, 15899507, 24894711, 38740189, 59929503, 92185390, 141029958, 214628608
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

Alternatively, number of partitions of 5n such that cn(2,5) = cn(3,5) <= cn(0,5) = cn(1,5) = cn(4,5).
For a given partition, cn(i,n) means the number of its parts equal to i modulo n.

Links

Formula

a(n) = A036882(n) - A036887(n)
a(n) = A036881(n) - A036885(n)
a(n) = A046776(n) + A036892(n)

Extensions

Terms a(10) onward from Max Alekseyev, Dec 11 2011

A036887 Number of partitions of 5n such that cn(1,5) = cn(4,5) <= cn(2,5) = cn(3,5) < cn(0,5).

Original entry on oeis.org

1, 2, 4, 10, 25, 62, 145, 323, 689, 1417, 2831, 5517, 10532, 19734, 36377, 66042, 118240, 208929, 364689, 629238, 1073964, 1814246, 3035236, 5031509, 8268583, 13476606, 21793642, 34981783, 55753411, 88258773, 138813831, 216978085, 337147547
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

Alternatively, number of partitions of 5n such that cn(2,5) = cn(3,5) <= cn(1,5) = cn(4,5) < cn(0,5).
For a given partition, cn(i,n) means the number of its parts equal to i modulo n.

Links

Formula

a(n) = A036882(n) - A036889(n)
a(n) = A202086(n) + A036895(n)

Extensions

Terms a(10) onward from Max Alekseyev, Dec 10 2011

A036891 Number of partitions of 5n such that cn(1,5) = cn(4,5) < cn(2,5) = cn(3,5) <= cn(0,5).

Original entry on oeis.org

0, 1, 4, 11, 26, 59, 129, 279, 588, 1216, 2451, 4836, 9326, 17641, 32746, 59795, 107507, 190634, 333661, 577104, 987043, 1670725, 2800269, 4650351, 7655282, 12497879, 20243241, 32543510, 51944000, 82345113, 129687646, 202974550, 315774972
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

Alternatively, number of partitions of 5n such that cn(2,5) = cn(3,5) < cn(1,5) = cn(4,5) <= cn(0,5).
For a given partition, cn(i,n) means the number of its parts equal to i modulo n.

Links

Formula

a(n) = A036892(n) + A036895(n)
a(n) = A036882(n) - A202085(n)

Extensions

Terms a(10) onward from Max Alekseyev, Dec 10 2011

A202085 Number of partitions of 5n such that cn(1,5) = cn(4,5) = cn(2,5) = cn(3,5) <= cn(0,5).

Original entry on oeis.org

1, 2, 4, 11, 28, 69, 153, 323, 647, 1258, 2380, 4427, 8092, 14601, 25991, 45724, 79469, 136604, 232235, 390806, 651132, 1074863, 1758595, 2853386, 4592952, 7337821, 11639376, 18337780, 28704122, 44653849, 69055688, 106188925, 162402533
Offset: 1

Views

Author

Max Alekseyev, Dec 11 2011

Keywords

Comments

For a given partition, cn(i,n) means the number of its parts equal to i modulo n.

Links

Formula

a(n) = A046776(n) + A202086(n)
a(n) = A036882(n) - A036891(n)

A202091 Number of partitions of 5n such that cn(1,5) = cn(4,5) and cn(2,5) = cn(3,5).

Original entry on oeis.org

1, 3, 11, 32, 88, 221, 532, 1213, 2672, 5676, 11724, 23568, 46315, 89076, 168124, 311763, 569000, 1023128, 1814776, 3178000, 5499588, 9411392, 15938221, 26726372, 44402336, 73121988, 119418609, 193488816, 311150404, 496783420, 787753316
Offset: 0

Views

Author

Max Alekseyev, Dec 11 2011

Keywords

Comments

For a given partition, cn(i,n) means the number of its parts equal to i modulo n.

Links

Crossrefs

Cf. A046776, A036880, A036881, A036882, A036883, A036884, A036885, A036886, A036887, A036888, A036889, A036890, A036891, A036892, A036893, A036894, A036895, A202085, A202086, A202087, A202088

Formula

a(n) = A046776(n) + A202086(n) + A202088(n) + 2*( A036886(n) + A036892(n) + A036893(n) + A036894(n) + A036895(n) )
a(n) = A202192(n) + 2*( A036886(n) + A036892(n) + A036893(n) + A036894(n) + A036895(n) )
Showing 1-5 of 5 results.

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