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 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. 3
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Alois P. Heinz, Rows n = 3..102, flattened FORMULA See program. EXAMPLE 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; 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 || n

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Last modified May 16 08:07 EDT 2021. Contains 343940 sequences. (Running on oeis4.)