A144212 -id:A144212 - 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

A144210 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 4; also row sums of A144209.

Original entry on oeis.org

1, 1, 1, 1, 4, 76, 1486, 29506, 628531, 14633011, 373486051, 10423892971, 316702467496, 10422938835196, 369779598658786, 14078057663869606, 572776958092098166, 24810200300393961286, 1140218754844983978646

Offset: 0

Alois P. Heinz, Sep 14 2008

nonn

			a(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.

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

A column of A144212. Cf. A144209.

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, Dec 02 2014, translated from Maple *)

a(n) = Sum_{k=0..n} A144209(n,k).

a(n) ~ c * n^(n-1), where c = 0.7519160836660874254... . - Vaclav Kotesovec, Sep 10 2014

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.

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