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 1-8 of 8 results.

A369222 Number of compositions (ordered partitions) of n into powers of 2 not greater than sqrt(n).

Original entry on oeis.org

1, 1, 1, 1, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 4930, 8651, 15182, 26642, 46754, 82047, 143983, 252672, 443409, 778128, 1365520, 2396320, 4205249, 7379697, 12950466, 22726483, 39882198, 69988378, 122821042, 215535903, 378239143, 663763424
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 16 2024

Keywords

Links

Crossrefs

Cf. A000045, A023359, A109696, A364526.

Programs

  • Maple
    b:= proc(n, t) option remember; `if`(n=0, 1,
      add(b(n-2^j, t), j=0..min(ilog2(n), t)))
    end:
a:= n-> b(n, ilog2(floor(sqrt(n)))):
seq(a(n), n=0..37);  # Alois P. Heinz, Jan 18 2024
  • Mathematica
    Table[SeriesCoefficient[1/(1 - Sum[Boole[IntegerQ[Log[2, k]]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 37}]

A368871 Number of compositions (ordered partitions) of n into odd parts not greater than sqrt(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 40893, 64208, 100816, 158296, 248548, 390257, 612761, 962125, 1510678, 2371987, 3724369, 5847808, 9181920, 14416967, 22636762, 35543051
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 08 2024

Keywords

Crossrefs

Cf. A000045, A364526.

Programs

  • Maple
    b:= proc(n, t) option remember; `if`(n=0, 1, add(
     `if`(j::odd, b(n-j, t), 0), j=1..min(n, t)))
    end:
a:= n-> b(n, floor(sqrt(n))):
seq(a(n), n=0..40);  # Alois P. Heinz, Jan 13 2024
  • Mathematica
    Table[SeriesCoefficient[1/(1 - Sum[Boole[OddQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 40}]

A368872 Number of compositions (ordered partitions) of n into prime parts not greater than sqrt(n).

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 1, 0, 1, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 2652, 3769, 5413, 7713, 11031, 15778, 22513, 32222, 46004, 65766, 94004, 134283, 191992, 274291, 392041, 560287, 800615, 1144320, 1635193, 2336976, 3339800, 4772784, 6821096
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 08 2024

Keywords

Crossrefs

Cf. A023360, A364526.

Programs

  • Maple
    b:= proc(n, t) option remember; `if`(n=0, 1, add(
     `if`(isprime(j), b(n-j, t), 0), j=1..min(n, t)))
    end:
a:= n-> b(n, floor(sqrt(n))):
seq(a(n), n=0..47);  # Alois P. Heinz, Jan 13 2024
  • Mathematica
    Table[SeriesCoefficient[1/(1 - Sum[Boole[PrimeQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 47}]

A368873 Number of compositions (ordered partitions) of n into nonprime parts not greater than sqrt(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 95, 131, 181, 250, 345, 476, 657, 907, 1252, 1728, 2385, 3292, 4544, 6272, 8657, 11949, 16493, 22765, 31422, 43371, 439373, 643932, 943728, 1383100, 2027032, 2970760, 4353861, 6380893, 9351653, 13705513, 20086406, 29438059
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 08 2024

Keywords

Crossrefs

Cf. A052284, A364526.

Programs

  • Maple
    b:= proc(n, t) option remember; `if`(n=0, 1, add(
     `if`(isprime(j), 0, b(n-j, t)), j=1..min(n, t)))
    end:
a:= n-> b(n, floor(sqrt(n))):
seq(a(n), n=0..47);  # Alois P. Heinz, Jan 13 2024
  • Mathematica
    Table[SeriesCoefficient[1/(1 - Sum[Boole[!PrimeQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 47}]

A369220 Number of compositions (ordered partitions) of n into squarefree parts not greater than sqrt(n).

Original entry on oeis.org

1, 1, 1, 1, 5, 8, 13, 21, 34, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415, 223317, 410744, 755476, 1389537, 4586976, 8662591, 16359466, 30895160, 58346092, 110187694, 208091537, 392984789, 742159180, 1401581598, 2646913261, 7359931330, 14066178853
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 16 2024

Keywords

Crossrefs

Cf. A280194, A364526.

Programs

  • Mathematica
    Table[SeriesCoefficient[1/(1 - Sum[Boole[SquareFreeQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 37}]

A369221 Number of compositions (ordered partitions) of n into prime power parts (not including 1) not greater than sqrt(n).

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 1, 0, 1, 5, 7, 9, 12, 16, 21, 28, 165, 241, 354, 518, 760, 1113, 1632, 2391, 3505, 14823, 22741, 34888, 53524, 82114, 125976, 193267, 296502, 454881, 697859, 1070626, 1642509, 2519868, 3865875, 5930862, 9098878, 13959114, 21415483, 32854729, 50404337, 77328204
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 16 2024

Keywords

Crossrefs

Cf. A280195, A364526.

Programs

  • Mathematica
    Table[SeriesCoefficient[1/(1 - Sum[Boole[PrimePowerQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 45}]

A369341 Number of compositions (ordered partitions) of n into triangular numbers not greater than sqrt(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 2823330, 4343681, 6682741, 10281375, 15817857, 24335721, 37440426, 57601964
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 20 2024

Keywords

Crossrefs

Cf. A023361, A364526.

Programs

  • Mathematica
    Table[SeriesCoefficient[1/(1 - Sum[x^(k (k + 1)/2), {k, 1, Floor[(Sqrt[1 + 8 Sqrt[n]] - 1)/2]}]), {x, 0, n}], {n, 0, 43}]

A369342 Number of compositions (ordered partitions) of n into squares not greater than sqrt(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 95, 131, 181, 250, 345, 476, 657, 907, 1252, 1728, 2385, 3292, 4544, 6272, 8657, 11949, 16493, 22765, 31422, 43371, 59864, 82629, 114051, 157422, 217286, 299915, 413966, 571388, 788674, 1088589, 1502555
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 20 2024

Keywords

Crossrefs

Cf. A006456, A364526.

Programs

  • Mathematica
    Table[SeriesCoefficient[1/(1 - Sum[x^(k^2), {k, 1, Floor[n^(1/4)]}]), {x, 0, n}], {n, 0, 46}]
Showing 1-8 of 8 results.

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