%I A057681
%S A057681 1,1,1,0,3,9,18,27,27,0,81,243,486,729,729,0,2187,6561,13122,19683,
%T A057681 19683,0,59049,177147,354294,531441,531441,0,1594323,4782969,9565938,
%U A057681 14348907,14348907,0,43046721,129140163,258280326,387420489,387420489
%V A057681 1,1,1,0,-3,-9,-18,-27,-27,0,81,243,486,729,729,0,-2187,-6561,-13122,-19683,
%W A057681 -19683,0,59049,177147,354294,531441,531441,0,-1594323,-4782969,-9565938,
%X A057681 -14348907,-14348907,0,43046721,129140163,258280326,387420489,387420489
%N A057681 Sum((-1)^j*binomial(n,3*j),j=0..floor(n/3)).
%H A057681 Ira Gessel, <a href="http://www.cs.brandeis.edu/~ira/">The Smith College 
               diploma problem</a>.
%F A057681 G.f.: (1-x)^2/((1-x)^3+x^3); a(n)=0^n/3+2*3^((n-2)/2)cos(pi*n/6). - Paul 
               Barry (pbarry(AT)wit.ie), Feb 26 2004
%F A057681 Binomial transform of (1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, ...) E.g.f. 
               : 2exp(3x/2)cos(sqrt(3)x/2)/3+1/3; a(n)=(((3+sqrt(-3))/2)^n+((3-sqrt(-3))/
               2)^n)/3+0^n/3. - Paul Barry (pbarry(AT)wit.ie), Feb 27 2004
%F A057681 a(n)=6a(n-1)-15a(n-2)+20a(n-3)-15a(n-4)+6a(n-5). - Paul Curtz (bpcrtz(AT)free.fr), 
               Jan 02 2008
%p A057681 A057681 := n->add((-1)^j*binomial(n,3*j),j=0..floor(n/3));
%Y A057681 Cf. A009116.
%Y A057681 Cf. A009545.
%Y A057681 Sequence in context: A112559 A030784 A123877 this_sequence A103312 A159794 
               A100967
%Y A057681 Adjacent sequences: A057678 A057679 A057680 this_sequence A057682 A057683 
               A057684
%K A057681 sign
%O A057681 0,5
%A A057681 N. J. A. Sloane (njas(AT)research.att.com), Oct 20 2000