A130213 Order of modular group of degree 3^(n-1) + 1.

0, 12, 360, 9828, 265680, 7174332, 193709880, 5230175508, 141214764960, 3812798732652, 102945566017800, 2779530283189188, 75047317648233840, 2026277576508690972, 54709494565753788120, 1477156353275409674868, 39883221538436233408320, 1076846981537778818585292

Offset

1,2

References

E. Mathieu, Mémoire sur le nombre de valeurs que peut acquérir une fonction quand on y permute ses variables de toutes les manières possibles, Journ. de math. (2) 5 (1860), 9-42 (see p. 39).

Links

Table of n, a(n) for n=1..18.

Ronald P. Nordgren, Compound Lucas Magic Squares, arXiv:2103.04774 [math.GM], 2021. See Table 2 p. 12.

Index entries for linear recurrences with constant coefficients, signature (30,-81).

Formula

a(n) = 3^(n-1)*(3^(2*n - 2) - 1)/2.

From Colin Barker, Sep 02 2013: (Start)

a(n) = 30*a(n-1) - 81*a(n-2).

G.f.: 12*x^2 / ((3*x-1)*(27*x-1)). (End)

Mathematica

Table[3^(x - 1) (3^(2 x - 2) - 1)/2, {x, 1, 15}]

Crossrefs

Cf. A120689.

Sequence in context: A128043 A012431 A012386 * A012633 A009079 A012379

Adjacent sequences: A130210 A130211 A130212 * A130214 A130215 A130216

Keyword

nonn,easy

Author

Artur Jasinski, Aug 04 2007

Extensions

More terms from Colin Barker, Sep 02 2013

Status

approved