A377946 Cogrowth sequence of the 16-element group C2^2:C4 = <S,T | S^4, T^2, (ST)^2, (S^2T)^2>.

1, 1, 2, 10, 40, 136, 512, 2080, 8320, 32896, 131072, 524800, 2099200, 8390656, 33554432, 134225920, 536903680, 2147516416, 8589934592, 34359869440, 137439477760, 549756338176, 2199023255552, 8796095119360, 35184380477440, 140737496743936, 562949953421312

Offset

0,3

Comments

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

Also called K8:C2. Gap identifier 16, 3.

Links

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

Formula

G.f.: (12*x^4-14*x^3+8*x^2-5*x+1) / ((4*x-1) * (2*x-1) * (4*x^2+1)).

Mathematica

CoefficientList[Series[(12*x^4-14*x^3+8*x^2-5*x+1)/((4*x-1)*(2*x-1)*(4*x^2+1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 10 2025 *)

Prog

(Magma) m:=35; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (12*x^4-14*x^3+8*x^2-5*x+1) / ((4*x-1) * (2*x-1) * (4*x^2+1)))); // Vincenzo Librandi, Oct 10 2025

Crossrefs

Cf. A377855 (C4:C4), A054879 (C2^3), A377843 (C4 X C2^2), A377943 (C4 o D4).

Sequence in context: A244376 A009338 A261473 * A174395 A320526 A193519

Adjacent sequences: A377943 A377944 A377945 * A377947 A377948 A377949

Keyword

nonn,easy

Author

Sean A. Irvine, Nov 11 2024

Status

approved