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 1-6 of 6 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)).

A377656 Cogrowth sequence of the 12-element dicyclic group Dic12 = .

Original entry on oeis.org

1, 0, 0, 0, 1, 5, 7, 7, 19, 39, 95, 187, 323, 663, 1351, 2755, 5579, 10863, 21679, 43643, 87411, 175399, 349591, 697843, 1397787, 2796255, 5595135, 11187435, 22362691, 44735255, 89480167, 178966627, 357936619, 715798479, 1431613775, 2863328347, 5726658323
Offset: 0

Views

Author

Sean A. Irvine, Nov 03 2024

Keywords

Examples

			a(5) = 5 corresponds to the words SSSTT = TSSST = TTSSS = STTSS = SSTTS = 1.

Crossrefs

Cf. A007583 (D6), A377626 (A4), A377627 (C6 x C2).

A377714 Cogrowth sequence for the 8-element group C4 X C2 = .

Original entry on oeis.org

1, 1, 2, 16, 72, 256, 992, 4096, 16512, 65536, 261632, 1048576, 4196352, 16777216, 67100672, 268435456, 1073774592, 4294967296, 17179738112, 68719476736, 274878431232, 1099511627776, 4398044413952, 17592186044416, 70368752566272, 281474976710656
Offset: 0

Views

Author

Sean A. Irvine, Nov 04 2024

Keywords

Comments

Gives the even terms, all odd terms are 0.

Examples

			a(2)=2 corresponds to the words SSSS = TTTT = 1.

Crossrefs

Cf. A377627 (C6 X C2).

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).

A378031 Cogrowth sequence for the 18-element group C6 X C3 = .

Original entry on oeis.org

1, 1, 2, 85, 926, 5461, 37130, 349525, 2973350, 22369621, 174174002, 1431655765, 11582386286, 91625968981, 729520967450, 5864062014805, 47006639297270, 375299968947541, 2999857885752002, 24019198012642645, 192222214478506046, 1537228672809129301
Offset: 0

Views

Author

Sean A. Irvine, Nov 14 2024

Keywords

Comments

Sequence gives terms for n = 0 (mod 3), all other terms are 0.

Crossrefs

Cf. A095364 (D9), A377627 (C6 X C2), A007613 (C3 X C3), A378109 (S3 X C3), A378110 (S3:C3).

Formula

G.f.: (36*x^4+99*x^3-14*x^2+6*x-1) / ((8*x-1) * (x+1) * (27*x^2+1)).

A378254 Cogrowth sequence of the 20-element group C10 X C2 = .

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 67, 1002, 8009, 43759, 184758, 646878, 1971883, 5541966, 16231216, 60090032, 290305577, 1523150157, 7564006759, 34099637859, 139541849878, 526321168143, 1878476551128, 6603812572941, 24052434515891, 94278969044262, 396750746960712
Offset: 0

Views

Author

Sean A. Irvine, Nov 20 2024

Keywords

Comments

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

Crossrefs

Cf. A377840 (C8 X C2), A377627 (C6 X C2), A078789 (D10).

Formula

G.f.: (10*x^9+75*x^8+162*x^7-48*x^6+127*x^5-126*x^4+84*x^3-36*x^2+9*x-1) / ((4*x-1) * (25*x^4+10*x^2-5*x+1) * (x^4+4*x^3+6*x^2-x+1)).
Showing 1-6 of 6 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.