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A129549
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Dimension of space of measures of entanglement that are homogeneous of degree 2n, for the case of four qubits.
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3
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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
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OFFSET
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0,2
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REFERENCES
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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.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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FORMULA
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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.
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MAPLE
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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);
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CROSSREFS
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Cf. A000217, A129548.
Sequence in context: A196741 A196899 A006411 * A171673 A185065 A092786
Adjacent sequences: A129546 A129547 A129548 * A129550 A129551 A129552
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KEYWORD
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nonn
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AUTHOR
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Mike Zabrocki, Apr 20 2007
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EXTENSIONS
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Revised definition and new Maple code from N. J. A. Sloane, Jun 17 2011
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STATUS
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approved
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