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 A129549 Dimension of space of measures of entanglement that are homogeneous of degree 2n, for the case of four qubits. 3
 1, 3, 20, 78, 352, 1365, 5232, 18271, 60598, 187296, 548020, 1515265, 3991204, 10035401, 24210308, 56188768, 125904351, 273044682, 574635828, 1176027747, 2345376048, 4565886531, 8691118644, 16198834634, 29602895824, 53105875363 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES 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. Nolan Wallach, The Hilbert series of measures of entanglement for 4 q-bits, Acta Appl. Math. 86(2005), 203-220. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA 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. MAPLE t1:=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 + 18275*q^28 + 16177*q^30 + 12876*q^32 + 9157*q^34 + 5660*q^36 + 3119*q^38 + 1539*q^40 + 654*q^42 + 219*q^44 + 76*q^46 + 20*q^48 + 3*q^50 + q^54; t2:=(1-q^2)^3*(1-q^4)^11*(1-q^6)^6; t3:=t1/t2; t4:=subs(q=sqrt(x), t3); t5:=series(t4, x, 30); CROSSREFS Cf. A000217, A129548. Sequence in context: A196741 A196899 A006411 * A171673 A185065 A092786 Adjacent sequences:  A129546 A129547 A129548 * A129550 A129551 A129552 KEYWORD nonn AUTHOR Mike Zabrocki, Apr 20 2007 EXTENSIONS Revised definition and new Maple code from N. J. A. Sloane, Jun 17 2011 STATUS approved

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