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.

A348644 a(n) = (18*n + 1)*(24*n + 1)*(144*n + 11).

Original entry on oeis.org

11, 73625, 542087, 1778645, 4156547, 8049041, 13829375, 21870797, 32546555, 46229897, 63294071, 84112325, 109057907, 138504065, 172824047, 212391101, 257578475, 308759417, 366307175, 430594997, 501996131, 580883825, 667631327, 762611885, 866198747, 978765161, 1100684375
Offset: 0

Views

Author

Michel Marcus, Oct 27 2021

Keywords

Comments

a(n) is the entry (1,2) of a family of unimodular matrices none of whose entries is 1 or -1, such that when each entry of the matrix is replaced by its cube, the resulting matrix is also unimodular.
In these matrices, the entries (1,3) and (3,1) = 2; the entries (2,3) and (3,2) = 3; the entry (3,3) = 0.

Links

Crossrefs

Cf. A000004, A007395, A010701, A348643, A348645, A348646.

Programs

  • PARI
    a(n) = (18*n + 1)*(24*n + 1)*(144*n + 11);

Formula

From Elmo R. Oliveira, Sep 03 2025: (Start)
G.f.: (11 + 73581*x + 247653*x^2 + 52003*x^3)/(x-1)^4.
E.g.f.: (11 + 73614*x + 197424*x^2 + 62208*x^3)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

A348645 a(n) = (12*n + 1)*(5184*n^2 + 540*n + 13).

Original entry on oeis.org

13, 74581, 545725, 1786693, 4170733, 8071093, 13861021, 21913765, 32602573, 46300693, 63381373, 84217861, 109183405, 138651253, 172994653, 212586853, 257801101, 309010645, 366588733, 430908613, 502343533, 581266741, 668051485, 763071013, 866698573, 979307413, 1101270781
Offset: 0

Views

Author

Michel Marcus, Oct 27 2021

Keywords

Comments

a(n) is the entry (2,1) of a family of unimodular matrices none of whose entries is 1 or -1, such that when each entry of the matrix is replaced by its cube, the resulting matrix is also unimodular.
In these matrices, the entries (1,3) and (3,1) = 2; the entries (2,3) and (3,2) = 3; the entry (3,3) = 0.

Links

Crossrefs

Cf. A000004, A007395, A010701, A348643, A348644, A348646.

Programs

  • PARI
    a(n) = (12*n + 1)*(5184*n^2 + 540*n + 13);

Formula

From Elmo R. Oliveira, Sep 04 2025: (Start)
G.f.: (13 + 74529*x + 247479*x^2 + 51227*x^3)/(x-1)^4.
E.g.f.: (13 + 74568*x + 198288*x^2 + 62208*x^3)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

A348646 a(n) = (72*n + 5)*(1296*n^2 + 153*n + 4).

Original entry on oeis.org

20, 111881, 818606, 2680067, 6256136, 12106685, 20791586, 32870711, 48903932, 69451121, 95072150, 126326891, 163775216, 207976997, 259492106, 318880415, 386701796, 463516121, 549883262, 646363091, 753515480, 871900301, 1002077426, 1144606727, 1300048076, 1468961345, 1651906406
Offset: 0

Views

Author

Michel Marcus, Oct 27 2021

Keywords

Comments

a(n) is the entry (2,2) of a family of unimodular matrices none of whose entries is 1 or -1, such that when each entry of the matrix is replaced by its cube, the resulting matrix is also unimodular.
In these matrices, the entries (1,3) and (3,1) = 2; the entries (2,3) and (3,2) = 3; the entry (3,3) = 0.

Links

Crossrefs

Cf. A000004, A007395, A010701, A348643, A348644, A348645.

Programs

  • PARI
    a(n) = (72*n + 5)*(1296*n^2 + 153*n + 4);

Formula

From Elmo R. Oliveira, Sep 04 2025: (Start)
G.f.: (20 + 111801*x + 371202*x^2 + 76849*x^3)/(x-1)^4.
E.g.f.: (20 + 111861*x + 297432*x^2 + 93312*x^3)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
Showing 1-3 of 3 results.

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