A377944 Cogrowth sequence of the 16-element dicyclic group Q16 = <S,T | S^8, T^4, (ST)^4, TST^3S>.

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

0,4

Comments

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

Also called Dic16, C8:C2. Gap identifier 16, 9.

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,4,16).

Formula

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

Mathematica

CoefficientList[Series[((6*x^3+3*x^2+2*x-1)/((4*x-1)*(4*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!( (6*x^3+3*x^2+2*x-1) / ((4*x-1) * (4*x^2+2*x+1)))); // Vincenzo Librandi, Oct 10 2025

Crossrefs

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

Sequence in context: A351104 A340685 A203026 * A189539 A000546 A130516

Adjacent sequences: A377941 A377942 A377943 * A377945 A377946 A377947

Keyword

nonn,easy

Author

Sean A. Irvine, Nov 11 2024

Status

approved