A377883 Cogrowth sequence of the 16-element modular group M4(2) = <S,T | S^8, T^2, STS^3T>.

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

0,4

Comments

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

Also called M16, C4.C4. Gap identifier 16,6.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-14,32,-40,32).

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)).

Mathematica

CoefficientList[Series[(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)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 10 2025 *)

Prog

(Magma) m:=35; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((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)))); // Vincenzo Librandi, Oct 10 2025

Crossrefs

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

Sequence in context: A071598 A224036 A120470 * A036423 A147827 A036632

Adjacent sequences: A377880 A377881 A377882 * A377884 A377885 A377886

Keyword

nonn,easy

Author

Sean A. Irvine, Nov 10 2024

Status

approved