A378110 Cogrowth sequence of the 18-element group S3:C3 = <S,T,U | S^3, T^3, U^2, (SU)^2, (TU)^2, [S,T]>.

1, 0, 1, 2, 5, 10, 53, 98, 397, 1058, 3341, 9658, 30053, 87386, 267877, 793682, 2397437, 7162066, 21552125, 64506026, 193839445, 580889738, 1743836117, 5229312706, 15692323949, 47067796610, 141222563821, 423628907162, 1270962692165, 3812740639930

Offset

0,4

Comments

Also called: C3^2:C2. Gap identifier 18, 4.

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,6,10,3,-18).

Formula

G.f.: (6*x^5-4*x^4-8*x^3-5*x^2+1) / ((x-1) * (3*x-1) * (2*x+1) * (3*x^2+2*x+1)).

Mathematica

CoefficientList[Series[(6*x^5-4*x^4-8*x^3-5*x^2+1)/((x-1)*(3*x-1)*(2*x+1)*(3*x^2+2*x+1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 09 2025 *)

Prog

(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (6*x^5-4*x^4-8*x^3-5*x^2+1)/((x-1)*(3*x-1)*(2*x+1)*(3*x^2+2*x+1)))); // Vincenzo Librandi, Oct 09 2025

Crossrefs

Cf. A095364 (D9), A378031 (C6 X C3), A378109 (S3 X C3), A001045 (S3).

Sequence in context: A124664 A076776 A020755 * A018503 A018535 A140304

Adjacent sequences: A378107 A378108 A378109 * A378111 A378112 A378113

Keyword

nonn,easy

Author

Sean A. Irvine, Nov 16 2024

Status

approved