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.

A202088 Number of partitions of 5n such that cn(0,5) < cn(1,5) = cn(4,5) = cn(2,5) = cn(3,5).

Original entry on oeis.org

0, 0, 1, 4, 11, 25, 55, 116, 245, 505, 1026, 2030, 3936, 7450, 13837, 25210, 45206, 79831, 139136, 239471, 407582, 686346, 1144532, 1890837, 3096692, 5029412, 8104448, 12961576, 20582130, 32459992, 50859769, 79192204, 122572743
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. A036888, A036893, A046776, A202087.

Programs

  • PARI
    seq(n)={Vec(sum(k=0, n\2, x^(2*k)*(1-x^k)/prod(j=1, k, 1 - x^j + O(x*x^n))^5) + O(x*x^n), -(n+1))} \\ Andrew Howroyd, Sep 16 2019

Formula

a(n) = A036888(n) - A036893(n).
a(n) = A202087(n) - A046776(n).
G.f.: Sum_{k>=0} x^(2*k)*(1-x^k)/(Product_{j=1..k} 1 - x^j)^5. - Andrew Howroyd, Sep 16 2019

Extensions

a(0)=0 prepended by Andrew Howroyd, Sep 16 2019

A036886 Number of partitions of 5n such that cn(0,5) = cn(1,5) = cn(4,5) < cn(2,5) = cn(3,5).

Original entry on oeis.org

1, 3, 6, 13, 27, 61, 132, 285, 590, 1190, 2325, 4441, 8288, 15197, 27394, 48679, 85332, 147790, 253016, 428602, 718696, 1193779, 1964996, 3206966, 5191350, 8339001, 13296592, 21053380, 33112242, 51746168, 80372146, 124104612, 190557592
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

Alternatively, number of partitions of 5n such that cn(0,5) = cn(2,5) = cn(3,5) < 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) = A036884(n) - A046776(n)
a(n) = A036885(n) - A036894(n)
a(n) = A036883(n) - A036893(n)

Extensions

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

A036883 Number of partitions of 5n such that cn(0,5) <= cn(1,5) = cn(4,5) < cn(2,5) = cn(3,5).

Original entry on oeis.org

1, 3, 7, 18, 45, 112, 263, 594, 1284, 2684, 5442, 10761, 20802, 39431, 73410, 134469, 242633, 431772, 758448, 1316294, 2258665, 3834699, 6445463, 10731790, 17709476, 28977664, 47036030, 75767355, 121164398, 192422933, 303572061, 475900075
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

Alternatively, number of partitions of 5n such that cn(0,5) <= cn(2,5) = cn(3,5) < 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) = A036880(n) - A202087(n)
a(n) = A036886(n) + A036893(n)

Extensions

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

A036888 Number of partitions of 5n such that cn(0,5) < cn(1,5) = cn(4,5) <= cn(2,5) = cn(3,5).

Original entry on oeis.org

0, 1, 5, 16, 43, 106, 247, 554, 1199, 2520, 5147, 10256, 19964, 38071, 71226, 130996, 237132, 423118, 744903, 1295274, 2226315, 3785452, 6371304, 10621516, 17547538, 28743111, 46701014, 75296105, 120512148, 191536534, 302392119, 474368206
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

Alternatively, number of partitions of 5n such that cn(0,5) < cn(2,5) = cn(3,5) <= 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) = A202088(n) + A036893(n)
a(n) = A036880(n) - A036884(n)

Extensions

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

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.

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

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