A242447 -id:A242447 - cp's OEIS frontend

A243124 Number of compositions of n in which the maximal multiplicity of parts equals 7.

1, 0, 8, 8, 44, 80, 236, 513, 1246, 2780, 6280, 13786, 30070, 64696, 134585, 285384, 594786, 1207084, 2453682, 4972098, 9946044, 19646041, 38691878, 75939596, 147425468, 283809162, 546291230, 1042095956, 1977521091, 3730060870, 7022446786, 13104269980

Offset: 7

Alois P. Heinz, May 29 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Column k=7 of A242447.

b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
    end:
a:= n-> b(n$2, 0, 7) -b(n$2, 0, 6):
seq(a(n), n=7..50);

a(n) = A243085(n) - A243084(n) = A243081(n,7) - A243081(n,6).

A243125 Number of compositions of n in which the maximal multiplicity of parts equals 8.

Original entry on oeis.org

1, 0, 9, 9, 54, 99, 309, 684, 1720, 3918, 9081, 20343, 45261, 99063, 214719, 460428, 965980, 2040096, 4255851, 8706522, 17810088, 36275538, 73017027, 145692324, 289702678, 573412764, 1124242476, 2191850439, 4259718588, 8229423030, 15785908575, 30199934205

Offset: 8

Alois P. Heinz, May 29 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 8..1000

Column k=8 of A242447.

b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
    end:
a:= n-> b(n$2, 0, 8) -b(n$2, 0, 7):
seq(a(n), n=8..50);

a(n) = A243086(n) - A243085(n) = A243081(n,8) - A243081(n,7).

A243126 Number of compositions of n in which the maximal multiplicity of parts equals 9.

Original entry on oeis.org

1, 0, 10, 10, 65, 120, 395, 890, 2320, 5401, 12857, 29435, 66955, 149455, 330042, 719882, 1554760, 3326365, 7009606, 14772370, 30835912, 63443345, 130298990, 266321547, 538824877, 1082905293, 2168501310, 4319287751, 8538816117, 16795672263, 32926171923

Offset: 9

Alois P. Heinz, May 29 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 9..1000

Column k=9 of A242447.

b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
    end:
a:= n-> b(n$2, 0, 9) -b(n$2, 0, 8):
seq(a(n), n=9..50);

a(n) = A243087(n) - A243086(n) = A243081(n,9) - A243081(n,8).

A243127 Number of compositions of n in which the maximal multiplicity of parts equals 10.

Original entry on oeis.org

1, 0, 11, 11, 77, 143, 495, 1133, 3058, 7271, 17777, 41591, 96767, 220473, 496661, 1103619, 2425929, 5276623, 11370986, 24294028, 51316156, 108047687, 225688551, 466237332, 960231624, 1967794950, 3997987950, 8077762209, 16258984885, 32550495175, 64759902032

Offset: 10

Alois P. Heinz, May 29 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 10..1000

Column k=10 of A242447.

b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
    end:
a:= n-> b(n$2, 0, 10) -b(n$2, 0, 9):
seq(a(n), n=10..50);

a(n) = A243088(n) - A243087(n) = A243081(n,10) - A243081(n,9).

cp's OEIS Frontend

A243124 Number of compositions of n in which the maximal multiplicity of parts equals 7.

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A243125 Number of compositions of n in which the maximal multiplicity of parts equals 8.

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Maple

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A243126 Number of compositions of n in which the maximal multiplicity of parts equals 9.

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Author

Keywords

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Crossrefs

Programs

Maple

Formula

A243127 Number of compositions of n in which the maximal multiplicity of parts equals 10.

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Author

Keywords

Links

Crossrefs

Programs

Maple

Formula