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

1, 2, 1, 8, 1, 32, 1, 128, 1, 512, 1, 2048, 1, 8192, 1, 32768, 1, 131072, 1, 524288, 1, 2097152, 1, 8388608, 1, 33554432, 1, 134217728, 1, 536870912, 1, 2147483648, 1, 8589934592, 1, 34359738368, 1, 137438953472, 1, 549755813888, 1, 2199023255552

Offset

1,2

Comments

Size of Frattini subgroup of the group of n X n signed permutations matrices (described in sequence A066051).

Links

Harry J. Smith, Table of n, a(n) for n = 1..350

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4).

Formula

G.f.: 1/(1-x^2) + 2*x*(1+2*x^2)/(1-2*x^2). - Paul Barry, Jun 17 2006

a(n) = 2^n*(1-(-1)^n)/2+(1+(-1)^n)/2. - Paul Barry, Jun 17 2006

E.g.f.: sinh(x) + sinh(x)^2. - Arkadiusz Wesolowski, Aug 13 2012

a(n) = (2 - (n mod 2))^(n - 1). - Wesley Ivan Hurt, Jul 21 2014

Maple

A066532:=n->(2 - (n mod 2))^(n - 1): seq(A066532(n), n=1..50); # Wesley Ivan Hurt, Jul 21 2014

Mathematica

Table[ If[ OddQ[n], 1, 2^(n - 1)], {n, 42} ]

Prog

(PARI) a(n) = { if (n%2, 1, 2^(n-1)) } \\ Harry J. Smith, Feb 22 2010

Crossrefs

Cf. A066051, A081294.

Sequence in context: A351708 A008309 A131175 * A205397 A020778 A118961

Adjacent sequences: A066529 A066530 A066531 * A066533 A066534 A066535

Keyword

nonn,easy

Author

Sharon Sela (sharonsela(AT)hotmail.com), Jan 06 2002

Extensions

More terms from Robert G. Wilson v, Jan 07 2002

More terms from Ralf Stephan, Jul 25 2003

Status

approved