A199476 Triangle read by rows: number of inequivalent classes of true tripartite entanglement systems of type 2 X M X N, for 2 <= N <= M.

2, 2, 6, 1, 5, 16, 1, 2, 12, 34, 1, 1, 6, 28, 77, 1, 1, 2, 14, 61, 157, 1, 1, 1, 6, 34, 133, 328, 1, 1, 1, 2, 15, 74, 277, 655, 1, 1, 1, 1, 6, 36, 165, 572, 1309, 1, 1, 1, 1, 2, 15, 80, 345, 1154, 2550, 1, 1, 1, 1, 1, 6, 37, 179, 722, 2299, 4958

Offset

2,1

Links

Table of n, a(n) for n=2..67.

XiKun Li, JunLi Li, Bin Liu and CongFeng Qiao, The parametric symmetry and numbers of the entangled class of 2 × M × N system, SCIENCE CHINA PHYSICS, MECHANICS & ASTRONOMY, Volume 54, Number 8, 1471-1475

Example

Triangle begins:
2
2 6
1 5 16
1 2 12 34
1 1 6 28 77
1 1 2 14 61 157
1 1 1 6 34 133 328
1 1 1 2 15 74 277 655
1 1 1 1 6 36 165 572 1309
...
This may also be regarded as a square array, allowing values on N >= M, in which case it begins like this:
2 2 1 1 1 1 1 1 1 ...
2 6 5 2 1 1 1 1 1 ...
1 5 16 12 6 2 1 1 1 ...
1 2 12 34 28 14 6 2 1 ...
1 1 6 28 77 61 34 15 6 ...
1 1 2 14 61 157 133 74 36 ...
1 1 1 6 34 133 328 277 165 ...
1 1 1 2 15 74 277 655 572 ...
1 1 1 1 6 36 165 572 1309 ...
...

Maple

f := proc(n, m)
    1/mul(1-x^k, k=1..m) ;
    coeftayl(%, x=0, n) ;
end proc:
F := proc(j, r, c)
    option remember ;
    if j < 0 then
        return 0 ;
    end if;
    if j = 0 then
        1 ;
    elif c = 0 then
        f(j, r) ;
    elif r=0 then
        f(j, c) ;
    else
        procname(j, r, 0)+procname(j, 0, c) + add(add(procname(j-m-n, m, n), n=1..c), m=1..r) ;
    end if ;
end proc:
omega := proc(M, N, i, j)
    option remember;
    A001970(2*M-N-3*i-j)*F(j, i, i+N-M) ;
end proc:
A199476 := proc(M, N)
    local a, i, j ;
    if N< M then
        return procname(N, M);
    end if;
    if N >= 2*M then
        return 1 ;
    end if;
    a := 0 ;
    for i from 0 to floor((2*M-N)/3) do
        for j from 0 to 2*M-N-3*i do
            a := a+ omega(M, N, i, j) ;
            if M = N and i =0 and j =0 then
                a := a-1 ;
            end if;
        end do:
    end do:
    a ;
end proc:
seq( seq(A199476(N, M), N=2..M), M=2..12) ; # R. J. Mathar, Feb 10 2024

Crossrefs

Cf. A199477.

Sequence in context: A101207 A186435 A260297 * A209124 A155818 A010245

Adjacent sequences: A199473 A199474 A199475 * A199477 A199478 A199479

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 06 2011

Status

approved