A350451 -id:A350451 - cp's OEIS frontend

A350449 Triangle read by rows: T(n,k) is the number of weakly connected acyclic digraphs on n unlabeled nodes with k arcs, n >= 1, k = 0..(n-1)*n/2.

1, 0, 1, 0, 0, 3, 1, 0, 0, 0, 8, 9, 6, 1, 0, 0, 0, 0, 27, 54, 79, 63, 33, 10, 1, 0, 0, 0, 0, 0, 91, 320, 732, 1136, 1281, 1056, 649, 281, 85, 15, 1, 0, 0, 0, 0, 0, 0, 350, 1788, 6012, 14378, 26529, 38407, 44621, 41638, 31321, 18843, 8983, 3325, 920, 180, 21, 1

Offset: 1

Andrew Howroyd, Dec 31 2021

			Triangle begins:
  [1] 1;
  [2] 0, 1;
  [3] 0, 0, 3, 1;
  [4] 0, 0, 0, 8,  9,  6,  1;
  [5] 0, 0, 0, 0, 27, 54, 79, 63, 33, 10, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 1..1350 (rows 1..20)

Row sums are A101228.
Columns sums are A350451.
Leading diagonal is A000238.
Cf. A350447 (not necessarily connected), A350450 (transpose).

\\ See PARI link in A122078 for program code.
{ my(T=WeakAcyclicDigraphsByArcs(6)); for(n=1, #T, print(T[n])) }

A350450 Triangle read by rows: T(n,k) is the number of unlabeled weakly connected acyclic digraphs with n arcs and k vertices, n >= 0, k = 1..n+1.

Original entry on oeis.org

1, 0, 1, 0, 0, 3, 0, 0, 1, 8, 0, 0, 0, 9, 27, 0, 0, 0, 6, 54, 91, 0, 0, 0, 1, 79, 320, 350, 0, 0, 0, 0, 63, 732, 1788, 1376, 0, 0, 0, 0, 33, 1136, 6012, 9933, 5743, 0, 0, 0, 0, 10, 1281, 14378, 45225, 54502, 24635, 0, 0, 0, 0, 1, 1056, 26529, 151848, 322736, 298250, 108968

Offset: 0

Andrew Howroyd, Dec 31 2021

			Triangle begins:
  1;
  0, 1;
  0, 0, 3;
  0, 0, 1, 8;
  0, 0, 0, 9, 27;
  0, 0, 0, 6, 54,   91;
  0, 0, 0, 1, 79,  320,  350;
  0, 0, 0, 0, 63,  732, 1788, 1376;
  0, 0, 0, 0, 33, 1136, 6012, 9933, 5743;
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..860 (rows 0..40)

Main diagonal is A000238.
Row sums are A350451.
Column sums are A101228.
Cf. A122078, A350449 (transpose).

\\ See PARI link in A122078 for program code.
{ my(T=WeakAcyclicDigraphsTr(10)); for(n=1, #T, print(T[n])); }

A101228 Number of weakly connected acyclic digraphs on n unlabeled nodes.

Original entry on oeis.org

1, 1, 4, 24, 267, 5647, 237317, 20035307, 3404385285, 1162502511721, 796392234736238, 1093228137893084112, 3004752537725051647790, 16527844667281561960220731, 181891583847006693859132403681, 4004313473818592854334088690859030

Offset: 1

Vladeta Jovovic, Jan 22 2005

nonn

The multiset transformation gives the number acyclic digraphs on n unlabeled nodes with k components:
;
, 1 ;
, 1 , 1 ;
, 5 , 1 , 1 ;
, 28 , 5 , 1 , 1 ;
, 301 , 29 , 5 , 1 , 1 ;
237317 , 6010 , 305 , 29 , 5 , 1 , 1 ; R. J. Mathar, Mar 21 2019

Andrew Howroyd, Table of n, a(n) for n = 1..50

Row sums of A350449.
Column sums of A350450.
Cf. A003087 (Euler trans.), A082402, A350451.

A350492 Number of unlabeled acyclic digraphs with n arcs and a global source and sink.

Original entry on oeis.org

1, 1, 1, 2, 5, 14, 44, 153, 584, 2414, 10732, 50909, 256198, 1360645, 7593530, 44366458, 270517289, 1716555943, 11308051214, 77170484915, 544525867544, 3965944595335, 29769162604337, 229970873746105, 1826057472681595, 14886348784740516

Offset: 0

Andrew Howroyd, Jan 08 2022

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..40

Column sums of A350491.

Cf. A122078, A345258, A350451, A350490.

A350492seq(20) \\ See PARI link in A122078 for program code.

A350490 Number of unlabeled acyclic digraphs with n arcs and a global source.

Original entry on oeis.org

1, 1, 2, 5, 15, 50, 191, 795, 3625, 17781, 93319, 519732, 3056185, 18880345, 122066437, 823118881, 5772473719, 41995743085, 316258151517, 2460542117337, 19743544526463, 163138014893817, 1386173917051704, 12096681529032989, 108293699332498981

Offset: 0

Andrew Howroyd, Jan 08 2022

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..40

Column sums of A350488.

Cf. A122078, A350415, A350451, A350492.

A350490seq(20) \\ See PARI link in A122078 for program code.

cp's OEIS Frontend

A350449 Triangle read by rows: T(n,k) is the number of weakly connected acyclic digraphs on n unlabeled nodes with k arcs, n >= 1, k = 0..(n-1)*n/2.

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A350450 Triangle read by rows: T(n,k) is the number of unlabeled weakly connected acyclic digraphs with n arcs and k vertices, n >= 0, k = 1..n+1.

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A101228 Number of weakly connected acyclic digraphs on n unlabeled nodes.

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A350492 Number of unlabeled acyclic digraphs with n arcs and a global source and sink.

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PARI

A350490 Number of unlabeled acyclic digraphs with n arcs and a global source.

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Author

Keywords

Links

Crossrefs

Programs

PARI