A061253 Let G_n be the elementary Abelian group G_n = (C_3)^n; a(n) is the number of times the number 1 appears in the character table of G_n.

5, 33, 261, 2241, 19845, 177633, 1595781, 14353281, 129153285, 1162300833, 10460471301, 94143533121, 847289672325, 7625600673633, 68630386930821, 617673424981761, 5559060652648965, 50031545357280033, 450283906665838341

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (12, -27).

Formula

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

From Chai Wah Wu, Jun 10 2020: (Start)

a(n) = 12*a(n-1) - 27*a(n-2) for n > 2.

G.f.: x*(5 - 27*x)/((3*x - 1)*(9*x - 1)). (End)

Example

a(1) = 5 because the character table of C_3 is / 1, 1, 1 / 1, z, z^2 / 1, z^2, z / where z = e^(2 * Pi * i /3) is a primitive cube root of unity.

Prog

(PARI) { for (n=1, 200, write("b061253.txt", n, " ", 3^(n-1) * (3^n + 2)) ) } \\ Harry J. Smith, Jul 20 2009

Crossrefs

Cf. A006516.

Sequence in context: A330802 A199552 A361411 * A111530 A367946 A087633

Adjacent sequences: A061250 A061251 A061252 * A061254 A061255 A061256

Keyword

nonn

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 02 2001

Extensions

More terms from Harry J. Smith, Jul 20 2009

Status

approved