A339160 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges and k nodes (n >= 1, 2 <= k <= n + 1).

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 1, 3, 6, 3, 1, 0, 1, 4, 11, 11, 4, 1, 0, 1, 5, 22, 33, 23, 5, 1, 0, 1, 7, 38, 89, 96, 40, 7, 1, 0, 1, 8, 63, 212, 345, 234, 70, 8, 1, 0, 1, 10, 98, 463, 1083, 1146, 546, 110, 10, 1, 0, 1, 12, 151, 943, 3068, 4739, 3505, 1169, 176, 12, 1, 0

Offset

1,12

Links

Andrew Howroyd, Table of n, a(n) for n = 1..210 (rows 1..20)

Formula

T(n,2) = T(n,n) = 1.

Example

Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
  1;
  1,  0;
  1,  1,   0;
  1,  1,   1,   0;
  1,  2,   2,   1,    0;
  1,  3,   6,   3,    1,    0;
  1,  4,  11,  11,    4,    1,    0;
  1,  5,  22,  33,   23,    5,    1,    0;
  1,  7,  38,  89,   96,   40,    7,    1,   0;
  1,  8,  63, 212,  345,  234,   70,    8,   1,  0;
  1, 10,  98, 463, 1083, 1146,  546,  110,  10,  1, 0;
  1, 12, 151, 943, 3068, 4739, 3505, 1169, 176, 12, 1, 0;
  ...

Crossrefs

Column k=3 is A001399(n-3).

Row sums are A010357.

Cf. A046752, A191646, A339070.

Sequence in context: A351995 A055290 A125629 * A355755 A141335 A133624

Adjacent sequences: A339157 A339158 A339159 * A339161 A339162 A339163

Keyword

nonn,tabl

Author

Andrew Howroyd, Dec 05 2020

Status

approved