A144212 Triangle T(n,k), n>=3, 3<=k<=n, read by rows: T(n,k) = number of simple graphs on n labeled nodes, where each maximally connected subgraph consists of a single node or has a unique cycle of length k.

2, 17, 4, 221, 76, 13, 3261, 1486, 433, 61, 54801, 29506, 11593, 2941, 361, 1049235, 628531, 296353, 102481, 23041, 2521, 22695027, 14633011, 7795873, 3270961, 1010881, 204121, 20161, 548904831, 373486051, 217126225, 104038201, 39355201

Offset: 3

Author

Alois P. Heinz, Sep 14 2008

Keywords

• nonn
• tabl
• look

Examples

			T(4,4) = 4, because there are 4 simple graphs on 4 labeled nodes, where each maximally connected subgraph consists of a single node or has a unique cycle of length 4:
.1.2. .1-2. .1-2. .1.2.
..... .|.|. ..X.. .|X|.
.3.4. .3-4. .3-4. .3.4.
Triangle begins:
        2;
       17,     4;
      221,    76,    13;
     3261,  1486,   433,   61;
    54801, 29506, 11593, 2941, 361;
		

Links

• Alois P. Heinz, Rows n = 3..102, flattened

Crossrefs

Columns k=3, 4 give: A144208, A144210. Diagonal gives: A139149. Cf. A053507, A065889, A098909, A144207, A144209, A007318, A000142.

Programs

Maple

B:= proc(n,c,k) option remember; if c=0 then 1 elif c<0 or n add(B(n,c,k), c=0..n): seq(seq(T(n,k), k=3..n), n=3..11);

Mathematica

B[n_, c_, k_] := B[n, c, k] = Which[c == 0, 1, c<0 || nJean-François Alcover, Jan 21 2014, translated from Alois P. Heinz's Maple code *)

Formula

See program.