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 1-8 of 8 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)).

A377855 Cogrowth sequence of the 16-element group C4:C4 = .

Original entry on oeis.org

1, 0, 2, 6, 40, 120, 512, 2016, 8320, 32640, 131072, 523776, 2099200, 8386560, 33554432, 134209536, 536903680, 2147450880, 8589934592, 34359607296, 137439477760, 549755289600, 2199023255552, 8796090925056, 35184380477440, 140737479966720, 562949953421312
Offset: 0

Views

Author

Sean A. Irvine, Nov 09 2024

Keywords

Comments

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

Links

Crossrefs

Cf. A070775 (C4 X C4), A377840 (C8 X C2).

Formula

G.f.: (12*x^4+6*x^3+2*x^2+2*x-1) / ((4*x-1) * (2*x+1) * (4*x^2+1)).

A377883 Cogrowth sequence of the 16-element modular group M4(2) = .

Original entry on oeis.org

1, 1, 1, 7, 34, 126, 496, 2052, 8264, 32776, 130816, 524272, 2098144, 8388576, 33550336, 134217792, 536887424, 2147483776, 8589869056, 34359738112, 137439215104, 549755813376, 2199022206976, 8796093023232, 35184376285184, 140737488357376, 562949936644096
Offset: 0

Views

Author

Sean A. Irvine, Nov 10 2024

Keywords

Comments

Gives the even terms, all the odd terms are 0.
Also called M16, C4.C4. Gap identifier 16,6.

Links

Crossrefs

Cf. A007582 (D8), A377840 (C8 X C2), A377855 (C4:C4), A377885 (SD16).

Formula

G.f.: (4*x^5-14*x^4+17*x^3-9*x^2+5*x-1) / ((4*x-1) * (4*x^2+1) * (2*x^2-2*x+1)).

A377885 Cogrowth sequence of the 16-element quasihedral group SD16 = .

Original entry on oeis.org

1, 1, 1, 4, 28, 136, 544, 2080, 8128, 32512, 130816, 524800, 2099200, 8390656, 33550336, 134201344, 536854528, 2147516416, 8590065664, 34359869440, 137438691328, 549754765312, 2199022206976, 8796095119360, 35184380477440, 140737496743936, 562949936644096
Offset: 0

Views

Author

Sean A. Irvine, Nov 10 2024

Keywords

Comments

Gives the even terms, all the odd terms are 0.
Also called QD16, Q8:C2. Gap identifier 16,8.

Links

Crossrefs

Cf. A047849 (D4), A007582 (D8), A071930 (Q8), A377840 (C8 X C2), A377883 (M4(2)).

Formula

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

A377735 Cogrowth sequence of the 16-element group Q8 X C2 = .

Original entry on oeis.org

1, 1, 7, 103, 829, 7261, 66595, 598627, 5377849, 48426745, 435876607, 3922582687, 35303534581, 317733991381, 2859598948507, 25736384863003, 231627537879409, 2084647743751921, 18761829221081335, 168856464809568727, 1519708183900618669, 13677373637498037325
Offset: 0

Views

Author

Sean A. Irvine, Nov 10 2024

Keywords

Comments

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

Links

Crossrefs

Cf. A047854 (D4 X C2), A377840 (C8 X C2), A071930 (Q8).

Formula

G.f.: (27*x^3+3*x^2+7*x-1) / ((1-x) * (9*x-1) * (9*x^2+2*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

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 1-8 of 8 results.

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

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