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 1-7 of 7 results.

A337548 Number of compositions (ordered partitions) of n into distinct parts congruent to 2 mod 3.

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 2, 1, 0, 4, 1, 6, 4, 1, 6, 6, 1, 12, 6, 1, 18, 8, 25, 24, 8, 25, 30, 10, 49, 42, 10, 73, 48, 12, 121, 60, 132, 145, 72, 134, 217, 84, 254, 265, 96, 376, 361, 114, 616, 433, 126, 858, 553, 864, 1218, 649, 882, 1580, 817, 1620, 2180, 937
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 22 2020

Keywords

Examples

			a(15) = 6 because we have [8, 5, 2], [8, 2, 5], [5, 8, 2], [5, 2, 8], [2, 8, 5] and [2, 5, 8].

Links

Crossrefs

Cf. A000931, A016789, A032020, A032021, A035386, A262928, A337547, A339059, A339060.

Programs

  • Mathematica
    nmax = 65; CoefficientList[Series[Sum[k! x^(k (3 k + 1)/2)/Product[1 - x^(3 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(3*k + 1)/2) / Product_{j=1..k} (1 - x^(3*j)).

A339059 Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 4.

Original entry on oeis.org

1, 1, 0, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 4, 6, 0, 1, 4, 6, 0, 1, 6, 12, 0, 1, 6, 18, 24, 1, 8, 24, 24, 1, 8, 30, 48, 1, 10, 42, 72, 1, 10, 48, 120, 121, 12, 60, 144, 121, 12, 72, 216, 241, 14, 84, 264, 361, 14, 96, 360, 601, 16, 114, 432, 841, 736, 126, 552, 1201, 738
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 22 2020

Keywords

Examples

			a(15) = 6 because we have [9, 5, 1], [9, 1, 5], [5, 9, 1], [5, 1, 9], [1, 9, 5] and [1, 5, 9].

Links

Crossrefs

Cf. A003269, A016813, A032020, A032021, A035451, A169975, A337547, A337548, A339060.

Programs

  • Mathematica
    nmax = 70; CoefficientList[Series[Sum[k! x^(k (2 k - 1))/Product[1 - x^(4 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(2*k - 1)) / Product_{j=1..k} (1 - x^(4*j)).

A339060 Number of compositions (ordered partitions) of n into distinct parts congruent to 3 mod 4.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 4, 1, 0, 6, 4, 1, 0, 6, 6, 1, 0, 12, 6, 1, 0, 18, 8, 1, 24, 24, 8, 1, 24, 30, 10, 1, 48, 42, 10, 1, 72, 48, 12, 1, 120, 60, 12, 121, 144, 72, 14, 121, 216, 84, 14, 241, 264, 96, 16, 361, 360, 114, 16, 601, 432, 126, 18, 841
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 22 2020

Keywords

Examples

			a(21) = 6 because we have [11, 7, 3], [11, 3, 7], [7, 11, 3], [7, 3, 11], [3, 11, 7] and [3, 7, 11].

Links

Crossrefs

Cf. A004767, A017817, A032020, A032021, A035462, A147599, A337547, A337548, A339059.

Programs

  • Mathematica
    nmax = 75; CoefficientList[Series[Sum[k! x^(k (2 k + 1))/Product[1 - x^(4 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(2*k + 1)) / Product_{j=1..k} (1 - x^(4*j)).

A339086 Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 5.

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 0, 1, 4, 6, 0, 0, 1, 4, 6, 0, 0, 1, 6, 12, 0, 0, 1, 6, 18, 24, 0, 1, 8, 24, 24, 0, 1, 8, 30, 48, 0, 1, 10, 42, 72, 0, 1, 10, 48, 120, 120, 1, 12, 60, 144, 120, 1, 12, 72, 216, 240, 1, 14, 84, 264, 360, 1, 14, 96, 360, 600, 1, 16, 114
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 23 2020

Keywords

Examples

			a(18) = 6 because we have [11, 6, 1], [11, 1, 6], [6, 11, 1], [6, 1, 11], [1, 11, 6] and [1, 6, 11].

Links

Crossrefs

Cf. A003520, A016861, A032020, A032021, A109697, A280454, A337547, A337548, A339059, A339060, A339087, A339088, A339089.

Programs

  • Mathematica
    nmax = 78; CoefficientList[Series[Sum[k! x^(k (5 k - 3)/2)/Product[1 - x^(5 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(5*k - 3)/2) / Product_{j=1..k} (1 - x^(5*j)).

A339087 Number of compositions (ordered partitions) of n into distinct parts congruent to 4 mod 5.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 4, 1, 0, 0, 6, 4, 1, 0, 0, 6, 6, 1, 0, 0, 12, 6, 1, 0, 0, 18, 8, 1, 0, 24, 24, 8, 1, 0, 24, 30, 10, 1, 0, 48, 42, 10, 1, 0, 72, 48, 12, 1, 0, 120, 60, 12, 1, 120, 144, 72, 14, 1, 120, 216, 84, 14, 1, 240
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 23 2020

Keywords

Examples

			a(27) = 6 because we have [14, 9, 4], [14, 4, 9], [9, 14, 4], [9, 4, 14], [4, 14, 9] and [4, 9, 14].

Links

Crossrefs

Cf. A016897, A017827, A032020, A032021, A109700, A281243, A337547, A337548, A339059, A339060, A339086, A339088, A339089.

Programs

  • Mathematica
    nmax = 80; CoefficientList[Series[Sum[k! x^(k (5 k + 3)/2)/Product[1 - x^(5 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(5*k + 3)/2) / Product_{j=1..k} (1 - x^(5*j)).

A339088 Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 6.

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 4, 6, 0, 0, 0, 1, 4, 6, 0, 0, 0, 1, 6, 12, 0, 0, 0, 1, 6, 18, 24, 0, 0, 1, 8, 24, 24, 0, 0, 1, 8, 30, 48, 0, 0, 1, 10, 42, 72, 0, 0, 1, 10, 48, 120, 120, 0, 1, 12, 60, 144, 120, 0, 1, 12, 72, 216, 240, 0, 1, 14, 84, 264, 360
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 23 2020

Keywords

Examples

			a(21) = 6 because we have [13, 7, 1], [13, 1, 7], [7, 13, 1], [7, 1, 13], [1, 13, 7] and [1, 7, 13].

Links

Crossrefs

Cf. A005708, A016921, A032020, A032021, A109701, A280456, A337547, A337548, A339059, A339060, A339086, A339087, A339089.

Programs

  • Mathematica
    nmax = 83; CoefficientList[Series[Sum[k! x^(k (3 k - 2))/Product[1 - x^(6 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(3*k - 2)) / Product_{j=1..k} (1 - x^(6*j)).

A339089 Number of compositions (ordered partitions) of n into distinct parts congruent to 5 mod 6.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 4, 1, 0, 0, 0, 6, 4, 1, 0, 0, 0, 6, 6, 1, 0, 0, 0, 12, 6, 1, 0, 0, 0, 18, 8, 1, 0, 0, 24, 24, 8, 1, 0, 0, 24, 30, 10, 1, 0, 0, 48, 42, 10, 1, 0, 0, 72, 48, 12, 1, 0, 0, 120, 60, 12, 1, 0, 120, 144
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 23 2020

Keywords

Examples

			a(33) = 6 because we have [17, 11, 5], [17, 5, 11], [11, 17, 5], [11, 5, 17], [5, 17, 11] and [5, 11, 17].

Links

Crossrefs

Cf. A016969, A017837, A032020, A032021, A109702, A281244, A337547, A337548, A339059, A339060, A339086, A339087, A339088.

Programs

  • Mathematica
    nmax = 86; CoefficientList[Series[Sum[k! x^(k (3 k + 2))/Product[1 - x^(6 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(3*k + 2)) / Product_{j=1..k} (1 - x^(6*j)).
Showing 1-7 of 7 results.

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