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.

A373962 Number of compositions of 6*n-2 into parts 5 and 6.

Original entry on oeis.org

0, 1, 3, 6, 10, 15, 22, 37, 81, 210, 550, 1354, 3096, 6646, 13655, 27490, 55523, 114516, 242652, 525221, 1147796, 2504932, 5423381, 11627959, 24732634, 52379410, 110882143, 235293738, 501101305, 1070653949, 2291969970, 4908426206, 10503741114, 22448059156
Offset: 1

Views

Author

Seiichi Manyama, Jun 24 2024

Keywords

Links

Crossrefs

Cf. A107025, A369794, A373961, A373963, A373964.
Cf. A017837.

Programs

  • Mathematica
    LinearRecurrence[{6,-15,20,-15,7,-1},{0,1,3,6,10,15},40] (* Harvey P. Dale, Nov 16 2024 *)
  • PARI
    a(n) = sum(k=0, n\5, binomial(n+k, n-2-5*k));

Formula

a(n) = A017837(6*n-2).
a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-2-5*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^2*(1-x)^3/((1-x)^6 - x^5).
a(n) = A373963(n+1) - A373963(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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