A129548 Measures of entanglement in 3-qbits.
1, 1, 8, 9, 36, 43, 120, 147, 329, 406, 784, 966, 1680, 2058, 3312, 4026, 6105, 7359, 10648, 12727, 17732, 21021, 28392, 33397, 43953, 51324, 66080, 76636, 96832, 111588, 138720, 158916, 194769, 221901, 268584, 304437, 364420, 411103, 487256, 547239, 642873
Offset: 0
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 Press, 2002.
Links
- Colin Barker, 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.
- Index entries for linear recurrences with constant coefficients, signature (2,4,-10,-5,20,0,-20,5,10,-4,-2,1).
Programs
-
Magma
[(2*n+3+(-1)^n)*(2*n+7+(-1)^n)*(2*n+11+(-1)^n)*(2*n^3+27*n^2+169*n+387-3*(n^2-5*n-31)*(-1)^n)/184320 : n in [0..50]]; // Wesley Ivan Hurt, Oct 15 2015
-
Maple
A129548:=n->(2*n+3+(-1)^n)*(2*n+7+(-1)^n)*(2*n+11+(-1)^n)*(2*n^3+27*n^2+169*n+387-3*(n^2-5*n-31)*(-1)^n)/184320: seq(A129548(n), n=0..50); # Wesley Ivan Hurt, Oct 15 2015
-
Mathematica
CoefficientList[Series[(x^2 - x + 1)*(x^2 + 1)/((1 - x)^7*(x + 1)^5), {x, 0, 50}], x] (* Wesley Ivan Hurt, Oct 15 2015 *) -
PARI
Vec(-(x^2-x+1)*(x^2+1)/((x-1)^7*(x+1)^5) + O(x^50)) \\ Colin Barker, Oct 15 2015
Formula
a(n) = [x^(2n)] (1+x^4)*(1+x^4+x^8)/((1-x^2)*(1-x^4)^5*(1-x^6)).
a(n) = (2*n+3+(-1)^n)*(2*n+7+(-1)^n)*(2*n+11+(-1)^n)*(2*n^3+27*n^2+169*n+387-3*(n^2-5*n-31)*(-1)^n)/184320. - Luce ETIENNE, Oct 15 2015.
From Colin Barker, Oct 15 2015: (Start)
a(n) = (n^6+24*n^5+280*n^4+1920*n^3+7504*n^2+14976*n+11520)/11520 (n even).
a(n) = (n^6+24*n^5+235*n^4+1200*n^3+3319*n^2+4536*n+2205)/11520 (n odd).
G.f.: -(x^2-x+1)*(x^2+1) / ((x-1)^7*(x+1)^5). (End)
a(n) = 2*a(n-1)+4*(n-2)-10*a(n-3)-5*a(n-4)+20*a(n-5)-20*a(n-7)+5*a(n-8)+10*a(n-9)-4*a(n-10)-2*a(n-11)+a(n-12) for n>11. - Wesley Ivan Hurt, Oct 15 2015