cp's OEIS Frontend

A066532 If n is odd a(n) = 1, if n is even a(n) = 2^(n-1).

%I A066532 #26 Dec 28 2024 19:34:17
%S A066532 1,2,1,8,1,32,1,128,1,512,1,2048,1,8192,1,32768,1,131072,1,524288,1,
%T A066532 2097152,1,8388608,1,33554432,1,134217728,1,536870912,1,2147483648,1,
%U A066532 8589934592,1,34359738368,1,137438953472,1,549755813888,1,2199023255552
%N A066532 If n is odd a(n) = 1, if n is even a(n) = 2^(n-1).
%C A066532 Size of Frattini subgroup of the group of n X n signed permutations matrices (described in sequence A066051).
%H A066532 Harry J. Smith, <a href="/A066532/b066532.txt">Table of n, a(n) for n = 1..350</a>
%H A066532 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-4).
%F A066532 G.f.: 1/(1-x^2) + 2*x*(1+2*x^2)/(1-2*x^2). - _Paul Barry_, Jun 17 2006
%F A066532 a(n) = 2^n*(1-(-1)^n)/2+(1+(-1)^n)/2. - _Paul Barry_, Jun 17 2006
%F A066532 E.g.f.: sinh(x) + sinh(x)^2. - _Arkadiusz Wesolowski_, Aug 13 2012
%F A066532 a(n) = (2 - (n mod 2))^(n - 1). - _Wesley Ivan Hurt_, Jul 21 2014
%p A066532 A066532:=n->(2 - (n mod 2))^(n - 1): seq(A066532(n), n=1..50); # _Wesley Ivan Hurt_, Jul 21 2014
%t A066532 Table[ If[ OddQ[n], 1, 2^(n - 1)], {n, 42} ]
%o A066532 (PARI) a(n) = { if (n%2, 1, 2^(n-1)) } \\ _Harry J. Smith_, Feb 22 2010
%Y A066532 Cf. A066051, A081294.
%K A066532 nonn,easy
%O A066532 1,2
%A A066532 Sharon Sela (sharonsela(AT)hotmail.com), Jan 06 2002
%E A066532 More terms from _Robert G. Wilson v_, Jan 07 2002
%E A066532 More terms from _Ralf Stephan_, Jul 25 2003