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 1-3 of 3 results.

A373961 Number of compositions of 6*n-1 into parts 5 and 6.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 15, 44, 129, 340, 804, 1742, 3550, 7009, 13835, 28033, 58993, 128136, 282569, 622575, 1357136, 2918449, 6204578, 13104675, 27646776, 58502733, 124411595, 265807567, 569552644, 1221316021, 2616456236, 5595314908, 11944318042, 25466629978
Offset: 1

Views

Author

Seiichi Manyama, Jun 23 2024

Keywords

Links

Crossrefs

Cf. A107025, A369794, A373962, A373963, A373964.
Cf. A017837.

Programs

  • PARI
    a(n) = sum(k=0, n\5, binomial(n+k, n-1-5*k));

Formula

a(n) = A017837(6*n-1).
a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-1-5*k).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 7*a(n-5) - a(n-6).
G.f.: x*(1-x)^4/((1-x)^6 - x^5).
a(n) = A373962(n+1) - A373962(n).

A373963 Number of compositions of 6*n-3 into parts 5 and 6.

Original entry on oeis.org

0, 0, 1, 4, 10, 20, 35, 57, 94, 175, 385, 935, 2289, 5385, 12031, 25686, 53176, 108699, 223215, 465867, 991088, 2138884, 4643816, 10067197, 21695156, 46427790, 98807200, 209689343, 444983081, 946084386, 2016738335, 4308708305, 9217134511, 19720875625
Offset: 1

Views

Author

Seiichi Manyama, Jun 24 2024

Keywords

Links

Crossrefs

Cf. A107025, A369794, A373961, A373962, A373964.
Cf. A017837.

Programs

  • PARI
    a(n) = sum(k=0, n\5, binomial(n+k, n-3-5*k));

Formula

a(n) = A017837(6*n-3).
a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-3-5*k).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 7*a(n-5) - a(n-6).
G.f.: x^3*(1-x)^2/((1-x)^6 - x^5).
a(n) = A373964(n+1) - A373964(n).

A373964 Number of compositions of 6*n-4 into parts 5 and 6.

Original entry on oeis.org

0, 0, 0, 1, 5, 15, 35, 70, 127, 221, 396, 781, 1716, 4005, 9390, 21421, 47107, 100283, 208982, 432197, 898064, 1889152, 4028036, 8671852, 18739049, 40434205, 86861995, 185669195, 395358538, 840341619, 1786426005, 3803164340, 8111872645, 17329007156
Offset: 1

Views

Author

Seiichi Manyama, Jun 24 2024

Keywords

Links

Crossrefs

Cf. A107025, A369794, A373961, A373962, A373963.
Cf. A017837.

Programs

  • PARI
    a(n) = sum(k=0, n\5, binomial(n+k, n-4-5*k));

Formula

a(n) = A017837(6*n-4).
a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-4-5*k).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 7*a(n-5) - a(n-6).
G.f.: x^4*(1-x)/((1-x)^6 - x^5).
a(n) = A369794(n+1) - A369794(n).
Showing 1-3 of 3 results.

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

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