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 1-4 of 4 results.

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)).

A377626 Cogrowth sequence of the 12-element group A4 = .

Original entry on oeis.org

1, 0, 1, 1, 1, 5, 4, 14, 21, 43, 91, 165, 354, 676, 1373, 2741, 5445, 10965, 21808, 43738, 87381, 174735, 349647, 698901, 1398318, 2796080, 5592445, 11185081, 22369145, 44740069, 89477724, 178957606, 357914197, 715826739, 1431658435, 2863308229, 5726626746
Offset: 0

Views

Author

Sean A. Irvine, Nov 02 2024

Keywords

Examples

			a(6)=4 corresponds to the words SSSSSS = TTTTTT = STSTST = TSTSTS = 1.

Crossrefs

Cf. A007583 (D6), A377627 (C6 x C2), A377656 (Dic2).

A378276 Cogrowth sequence of the 20-element dicyclic group Dic20 = .

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 6, 7, 19, 9, 61, 88, 226, 377, 945, 1473, 3427, 6154, 13758, 25327, 53967, 102865, 213345, 411700, 849706, 1661885, 3382821, 6668577, 13493719, 26725414, 53861446, 107074403, 215261971, 428704177, 860266725, 1715950208, 3439229842, 6866462849
Offset: 0

Views

Author

Sean A. Irvine, Nov 21 2024

Keywords

Crossrefs

Cf. A377656 (Dic12), A078789 (D10), A378254 (C10 X C2), A378278 (Frob20).

Formula

G.f.: (4*x^9-6*x^8-3*x^7-5*x^6-2*x^5-2*x^4-2*x^3-x^2+1) / ((2*x-1) * (2*x^2+2*x+1) * (x^2-x-1) * (4*x^4-2*x^3+3*x^2-x+1)).

A377944 Cogrowth sequence of the 16-element dicyclic group Q16 = .

Original entry on oeis.org

1, 0, 1, 12, 28, 120, 544, 2016, 8128, 33024, 130816, 523776, 2099200, 8386560, 33550336, 134234112, 536854528, 2147450880, 8590065664, 34359607296, 137438691328, 549756862464, 2199022206976, 8796090925056, 35184380477440, 140737479966720, 562949936644096
Offset: 0

Views

Author

Sean A. Irvine, Nov 11 2024

Keywords

Comments

Gives the even terms, all the odd terms are 0.
Also called Dic16, C8:C2. Gap identifier 16, 9.

Links

Crossrefs

Cf. A071930 (Q8), A377656 (Dic12), A377735 (Q8 X C2), A377840 (C8 X C2), A007582 (D8), A377885 (SD16), A377883 (M4(2)).

Formula

G.f.: (6*x^3+3*x^2+2*x-1) / ((4*x-1) * (4*x^2+2*x+1)).
Showing 1-4 of 4 results.

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

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