A339228
Triangle read by rows: T(n,k) is the number of oriented series-parallel networks with n colored elements using exactly k colors.
Original entry on oeis.org
1, 2, 3, 5, 22, 19, 15, 146, 321, 195, 48, 970, 4116, 5972, 2791, 167, 6601, 48245, 125778, 135235, 51303, 602, 46012, 546570, 2281528, 4238415, 3609966, 1152019, 2256, 328188, 6118320, 38437972, 109815445, 157612413, 111006329, 30564075
Offset: 1
Triangle begins:
1;
2, 3;
5, 22, 19;
15, 146, 321, 195;
48, 970, 4116, 5972, 2791;
167, 6601, 48245, 125778, 135235, 51303;
602, 46012, 546570, 2281528, 4238415, 3609966, 1152019;
...
-
\\ R(n,k) gives colorings using at most k colors as a vector.
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
R(n,k)={my(Z=k*x, p=Z+O(x^2)); for(n=2, n, p=x*Ser(EulerT(Vec(p^2/(1+p)+Z)))); Vec(p)}
M(n)={my(v=vector(n, k, R(n, k)~)); Mat(vector(n, k, sum(i=1, k, (-1)^(k-i)*binomial(k, i)*v[i])))}
{my(T=M(8)); for(n=1, #T~, print(T[n, 1..n]))}
A339226
Number of oriented series-parallel networks with n elements of 2 colors.
Original entry on oeis.org
2, 7, 32, 176, 1066, 6935, 47216, 332700, 2404818, 17734668, 132901644, 1009161505, 7747608480, 60037905076, 468987635982, 3689066578347, 29195587558726, 232303316402615, 1857264782113562, 14912673794505898, 120203145484455930, 972291038495626309
Offset: 1
In the following examples elements in series are juxtaposed and elements in parallel are separated by '|'.
a(1) = 2: (1), (2).
a(2) = 7: (11), (12), (21), (22), (1|1), (1|2), (2|2).
A339281
Number of unoriented series-parallel networks with n colored elements using exactly 2 colors.
Original entry on oeis.org
0, 2, 14, 84, 522, 3426, 23404, 165417, 1197934, 8847201, 66359672, 504180138, 3872043674, 30011312118, 234460670790, 1844390161675, 14597175479270, 116148990100435, 928620864502940, 7456287071153017, 60101357023288316, 486144584042042269, 3944839973878931780
Offset: 1
In the following examples elements in series are juxtaposed and elements in parallel are separated by '|'.
a(2) = 2: (12), (1|2).
a(3) = 14: (112), (121), (122), (212), (1(1|2)), (1(2|2)), (2(1|1)), (2(1|2)), (1|12), (1|22), (2|11), (2|12), (1|1|2), (1|2|2).
Showing 1-3 of 3 results.
Comments