A377855 Cogrowth sequence of the 16-element group C4:C4 = <S,T | S^4, T^4, STST^3>.

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

0,3

Comments

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

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,4,8,32).

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)).

Mathematica

CoefficientList[Series[(12*x^4+6*x^3+2*x^2+2*x-1)/((4*x-1)*(2*x+1)*(4*x^2+1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 11 2025 *)

Prog

(Magma) m:=35; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (12*x^4+6*x^3+2*x^2+2*x-1) / ((4*x-1) * (2*x+1) * (4*x^2+1)))); // Vincenzo Librandi, Oct 11 2025

Crossrefs

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

Sequence in context: A288491 A212883 A378272 * A336959 A027161 A081096

Adjacent sequences: A377852 A377853 A377854 * A377856 A377857 A377858

Keyword

nonn,easy

Author

Sean A. Irvine, Nov 09 2024

Status

approved