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.

A377840 Cogrowth sequence of the 16-element group C8 X C2 = .

Original entry on oeis.org

1, 1, 1, 1, 2, 46, 496, 3004, 12872, 43912, 130816, 394384, 1470944, 6874336, 33550336, 151869376, 622116992, 2353246336, 8589869056, 31961192704, 125858012672, 521796316672, 2199022206976, 9122012806144, 36758056208384, 144536687773696, 562949936644096
Offset: 0

Views

Author

Sean A. Irvine, Nov 09 2024

Keywords

Comments

Gives the even terms, all the odd terms are 0.

Examples

			a(4)=2 corresponds to the words SSSSSSSS and TTTTTTTT.

Links

Crossrefs

Cf. A007582 (D8), A377627 (C6 X C2), A377714 (C4 X C2).

Formula

G.f.: (8*x^7+28*x^6+42*x^5-34*x^4+35*x^3-21*x^2+7*x-1) / ((4*x-1) * (4*x^2+1) * (4*x^4+8*x^3+8*x^2-4*x+1)).

A377627 Cogrowth sequence of the 12-element group C6 X C2 = .

Original entry on oeis.org

1, 1, 1, 2, 29, 211, 926, 3095, 9829, 37130, 164921, 728575, 2973350, 11450531, 43942081, 174174002, 708653429, 2884834891, 11582386286, 46006694735, 182670807229, 729520967450, 2926800830801, 11743814559415, 47006639297270, 187791199242011, 750176293590361
Offset: 0

Views

Author

Sean A. Irvine, Nov 02 2024

Keywords

Comments

Gives the even terms, all the odd terms are 0.

Examples

			a(2)=1 corresponds to the word TTTT.
a(3)=2 corresponds to the words SSSSSS and TTTTTT.

Crossrefs

Cf. A007583 (D6), A377626 (A4), A377656 (Dic12), A377714 (C4 X C2), A377840 (C8 X C2).

Formula

G.f.: (6*x^5+5*x^4+11*x^3-10*x^2+5*x-1) / ((4*x-1) * (x^2+x+1) * (9*x^2-3*x+1)).

A377843 Cogrowth sequence of the 16-element group C4 X C2 X C2 = .

Original entry on oeis.org

1, 2, 9, 62, 689, 7322, 69369, 616982, 5422049, 48197042, 433434729, 3913915502, 35311723409, 317999340362, 2860994944089, 25738114039622, 231602961592769, 2084457277181282, 18761300850805449, 168858054223133342, 1519730933499158129, 13677470410291063802
Offset: 0

Views

Author

Sean A. Irvine, Nov 09 2024

Keywords

Comments

Gives the even terms, all the odd terms are 0.

Examples

			a(2)=9 corresponds to the words SSSS, TTTT, UUUU, TTUU, TUUT, UUTT, TUTU, UTUT, UTTU.

Links

Crossrefs

Cf. A070775 (C4 X C4), A377714 (C4 X C2), A377840 (C8 X C2), A007582 (D8).

Programs

  • Mathematica
    LinearRecurrence[{15,-78,210,79,-225},{1, 2, 9, 62, 689},22] (* James C. McMahon, Nov 10 2024 *)

Formula

G.f.: (38*x^4+127*x^3-57*x^2+13*x-1) / ((1-x) * (9*x-1) * (x+1) * (25*x^2-6*x+1)).
E.g.f.: (2*exp(3*x)*cos(4*x) + 5*cosh(x) + cosh(9*x) + sinh(x) + sinh(9*x))/8. - Stefano Spezia, Nov 10 2024
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.