A377885 Cogrowth sequence of the 16-element quasihedral group SD16 = <S,T | S^8, T^2, STS^5T>.

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

0,4

Comments

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

Also called QD16, Q8:C2. Gap identifier 16,8.

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,-12,16).

Formula

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

Mathematica

CoefficientList[Series[(6*x^3-7*x^2+5*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^3-7*x^2+5*x-1) / ((4*x-1) * (4*x^2-2*x+1)))); // Vincenzo Librandi, Oct 10 2025

Crossrefs

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

Sequence in context: A296638 A270721 A367015 * A270892 A271603 A139736

Adjacent sequences: A377882 A377883 A377884 * A377886 A377887 A377888

Keyword

nonn,easy

Author

Sean A. Irvine, Nov 10 2024

Status

approved