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

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

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.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Nolan Wallach, The Hilbert series of measures of entanglement for 4 q-bits, Acta Appl. Math. 86(2005), 203-220.

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); # N. J. A. Sloane, Jun 17 2011

Crossrefs

Cf. A000217, A129548.

Sequence in context: A196899 A006411 A243208 * A171673 A185065 A227811

Adjacent sequences: A129546 A129547 A129548 * A129550 A129551 A129552

Keyword

nonn

Author

Mike Zabrocki, Apr 20 2007

Extensions

Revised definition from N. J. A. Sloane, Jun 17 2011

Status

approved