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A071930 Number of words of length 2n in the two letters s and t that reduce to the identity 1 by using the relations ssTT=1, ststSS=1 and ststTT=1, where S and T are the inverses of s and t, respectively (i.e., sS=1 and tT=1). The generators s and t and the three stated relations generate the quaternion group Q4. 0
0, 6, 12, 72, 240, 1056, 4032, 16512, 65280, 262656, 1047552, 4196352, 16773120, 67117056, 268419072, 1073774592, 4294901760, 17180000256, 68719214592, 274878431232, 1099510579200, 4398048608256, 17592181850112 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = A003683(n+1)/6. No words of odd length (see the description above) reduce to 1.

LINKS

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (2,8).

FORMULA

a(n) = 2^(2n-2) - (-2)^(n-1).

a(1)=0, a(2)=6, a(n) = 2*a(n-1) + 8*a-(n-2). - Harvey P. Dale, Dec 10 2012

G.f.: -6*x/(8*x^2+2*x-1)). - Harvey P. Dale, Dec 10 2012

G.f.: Q(0), where Q(k)= 1 - 1/(4^k - 4*x*16^k/(4*x*4^k - 1/(1 + 1/(2*4^k - 16*x*16^k/(8*x*4^k +1/Q(k+1)))))); (continued fraction). - Sergei N. Gladkovskii, May 21 2013

MATHEMATICA

Table[2^(2n-2)-(-2)^(n-1), {n, 30}] (* or *) LinearRecurrence[{2, 8}, {0, 6}, 30] (* Harvey P. Dale, Dec 10 2012 *)

CROSSREFS

Cf. A003683.

Sequence in context: A088726 A163342 A107904 * A239854 A061520 A305058

Adjacent sequences:  A071927 A071928 A071929 * A071931 A071932 A071933

KEYWORD

nonn,easy

AUTHOR

John W. Layman and Jamaine Paddyfoot (jay_paddyfoot(AT)hotmail.com), Jun 14 2002

STATUS

approved

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Last modified February 22 19:59 EST 2019. Contains 320403 sequences. (Running on oeis4.)