A144207 -id:A144207 - cp's OEIS frontend

A144208 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 3; also row sums of A144207.

1, 1, 1, 2, 17, 221, 3261, 54801, 1049235, 22695027, 548904831, 14701691121, 432342705351, 13856514927207, 480891887472585, 17971038945463101, 719613541474095591, 30743125693699501431, 1395902175504288127695

Offset: 0

Alois P. Heinz, Sep 14 2008

nonn

			a(3) = 2, because there are 2 simple graphs on 3 labeled nodes, where each maximally connected subgraph consists of a single node or has a unique cycle of length 3:
.1.2. .1-2.
..... .|/..
.3... .3...

Alois P. Heinz, Table of n, a(n) for n = 0..150

Row sums of triangle A144207. A column of A144212. Cf. A053507, A007318.

T:= proc(n,k) option remember; if k=0 then 1 elif k<0 or n add(T(n,k), k=0..n): seq(a(n), n=0..23);

T[n_, k_] := T[n, k] = Which[k == 0, 1, k<0 || nJean-François Alcover, Feb 05 2015, after Alois P. Heinz *)

a(n) = Sum_{k=0..n} A144207(n,k).

a(n) ~ c * n^(n-1), where c = 0.762590842281789937101466... . - Vaclav Kotesovec, Sep 10 2014

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.

Original entry on oeis.org

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

Alois P. Heinz, Sep 14 2008

			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;

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

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

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);

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 *)

See program.

cp's OEIS Frontend

A144208 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 3; also row sums of A144207.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula