cp's OEIS Frontend

A129549 Dimension of space of measures of entanglement that are homogeneous of degree 2n, for the case of four qubits.

%I A129549 #20 Jul 24 2018 16:34:21
%S A129549 1,3,20,78,352,1365,5232,18271,60598,187296,548020,1515265,3991204,
%T A129549 10035401,24210308,56188768,125904351,273044682,574635828,1176027747,
%U A129549 2345376048,4565886531,8691118644,16198834634,29602895824,53105875363
%N A129549 Dimension of space of measures of entanglement that are homogeneous of degree 2n, for the case of four qubits.
%D A129549 David Meyer and Nolan Wallach, Invariants for multiple qubits: the case of 3 qubits, Mathematics of quantum computing, Computational Mathematics Series, 77-98, Chapman&Hall/CRC, 2002.
%H A129549 Alois P. Heinz, <a href="/A129549/b129549.txt">Table of n, a(n) for n = 0..1000</a>
%H A129549 Nolan Wallach, <a href="https://dx.doi.org/10.1007/s10440-005-0471-3">The Hilbert series of measures of entanglement for 4 q-bits</a>, Acta Appl. Math. 86(2005), 203-220.
%F A129549 a(n) = [q^(2n)] (P(q) + q^54*P(1/q))/((1 - q^2)^3*(1 - q^4)^11*(1 - q^6)^6) where P(q) = 1 + 3*q^4 + 20*q^6 + 76*q^8 + 219*q^10 + 654*q^12 + 1539*q^14 + 3119*q^16 + 5660*q^18 + 9157*q^20 + 12876*q^22 + 16177*q^24 + 18275*q^26.
%p A129549 t1:=1 + 3*q^4 + 20*q^6 + 76*q^8 + 219*q^10 + 654*q^12 +
%p A129549 1539*q^14 + 3119*q^16 + 5660*q^18 + 9157*q^20 +
%p A129549 12876*q^22 + 16177*q^24 + 18275*q^26 +
%p A129549 18275*q^28 + 16177*q^30 + 12876*q^32 +
%p A129549 9157*q^34 + 5660*q^36 + 3119*q^38 + 1539*q^40 +
%p A129549 654*q^42 + 219*q^44 + 76*q^46 + 20*q^48 + 3*q^50 + q^54;
%p A129549 t2:=(1-q^2)^3*(1-q^4)^11*(1-q^6)^6;
%p A129549 t3:=t1/t2;
%p A129549 t4:=subs(q=sqrt(x),t3);
%p A129549 t5:=series(t4,x,30); # _N. J. A. Sloane_, Jun 17 2011
%Y A129549 Cf. A000217, A129548.
%K A129549 nonn
%O A129549 0,2
%A A129549 _Mike Zabrocki_, Apr 20 2007
%E A129549 Revised definition from _N. J. A. Sloane_, Jun 17 2011