A378109 Cogrowth sequence of the 18-element group S3 X C3 = <S,T,U | S^3, T^2, U^3, (ST)^2, [S,U], [T,U]>.

1, 0, 1, 2, 3, 15, 32, 126, 351, 1094, 3321, 9801, 29768, 88452, 266085, 797162, 2390391, 7175547, 21516800, 64573362, 193700403, 581130734, 1743421725, 5230147077, 15690706952, 47071500840, 141215033961, 423644304722, 1270932117003, 3812799539655

Offset

0,4

Comments

Also called: D3 X C3. Gap identifier 18, 3.

Links

Table of n, a(n) for n=0..29.

Formula

G.f.: (3*x^8-3*x^6-16*x^5+6*x^4+7*x^3-2*x^2-3*x+1) / ((x-1) * (3*x-1) * (x^2+x+1) * (3*x^2+3*x+1) * (3*x^2-3*x+1)).

Crossrefs

Cf. A095364 (D9), A378031 (C6 X C3), A378110 (S3:C3), A001045 (S3).

Sequence in context: A064219 A244377 A244330 * A342867 A060753 A241198

Adjacent sequences: A378104 A378106 A378107 * A378110 A378112 A378113

Keyword

nonn,easy,new

Author

Sean A. Irvine, Nov 16 2024

Status

approved