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A007982 Number of non-Abelian metacyclic groups of order 2^n. 1
0, 0, 2, 5, 9, 15, 22, 32, 43, 57, 72, 91, 110, 134, 158, 187, 216, 251, 285, 326, 366, 413, 459, 513, 565, 626, 685, 753, 819, 895, 968, 1052, 1133, 1225, 1314, 1415, 1512, 1622, 1728, 1847, 1962, 2091, 2215, 2354, 2488, 2637, 2781, 2941, 3095, 3266, 3431 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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) = A136184(n) - floor(n/2) - 1. - Eric M. Schmidt, Jan 08 2015

G.f.: -x^3*(x^8+x^7-x^6-x^5+2*x^4+2*x^3-3*x-2) / ((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, 2, 5, 9, 15, 22, 32, 43, 57, 72}, 60] (* Harvey P. Dale, Oct 06 2016 *)

PROG

(PARI) concat([0, 0], Vec(-x^3*(x^8+x^7-x^6-x^5+2*x^4+2*x^3-3*x-2) / ((x-1)^4*(x+1)^2*(x^2+x+1)) + O(x^100))) \\ Colin Barker, Jan 12 2015

CROSSREFS

Sequence in context: A195014 A152738 A022941 * A011904 A218914 A047809

Adjacent sequences:  A007979 A007980 A007981 * A007983 A007984 A007985

KEYWORD

nonn,easy

AUTHOR

S. Liedahl

EXTENSIONS

a(2) corrected and sequence extended (using A136184) by Eric M. Schmidt, Jan 08 2015

STATUS

approved

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Last modified November 21 17:44 EST 2017. Contains 295004 sequences.