A007983 Number of non-Abelian metacyclic groups of order p^n (p odd).

0, 0, 1, 2, 4, 7, 10, 15, 20, 27, 34, 44, 53, 66, 78, 94, 109, 129, 147, 171, 193, 221, 247, 280, 310, 348, 383, 426, 466, 515, 560, 615, 666, 727, 784, 852, 915, 990, 1060, 1142, 1219, 1309, 1393, 1491, 1583, 1689, 1789, 1904, 2012, 2136, 2253, 2386, 2512

Offset

1,4

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Steven Liedahl, Enumeration of metacyclic p-groups, J. Algebra 186 (1996), no. 2, 436-446.

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-2,-1,2,1,-1).

Formula

a(n) = A136185(n) - floor(n/2) - 1. - Eric M. Schmidt, Jan 08 2015

G.f.: -x^3*(x^4-x-1) / ((x-1)^4*(x+1)^2*(x^2+x+1)). - Colin Barker, Jan 12 2015

Mathematica

LinearRecurrence[{1, 2, -1, -2, -1, 2, 1, -1}, {0, 0, 1, 2, 4, 7, 10, 15}, 60] (* Harvey P. Dale, Jun 17 2016 *)

Prog

(PARI) concat([0, 0], Vec(-x^3*(x^4-x-1)/((x-1)^4*(x+1)^2*(x^2+x+1)) + O(x^100))) \\ Colin Barker, Jan 12 2015

Crossrefs

Sequence in context: A027384 A022939 A036702 * A049640 A179385 A362040

Adjacent sequences: A007980 A007981 A007982 * A007984 A007985 A007986

Keyword

nonn,easy

Author

S. Liedahl

Extensions

Initial terms added and sequence extended (using A136185) by Eric M. Schmidt, Jan 08 2015

Status

approved