A369283 -id:A369283 - cp's OEIS frontend

A102579 Number of n-node labeled digraphs whose underlying graphs are mating graphs, cf. A006024.

1, 1, 3, 36, 2160, 577260, 629332740, 2778611237640, 49231195558057800, 3472536190055702938560, 971496134741368475512176960, 1076456769176854177692230640971520, 4723714896453453856832035698858163891200, 82155195331101404797144020808246647196388279040

Offset: 0

Goran Kilibarda, Zoran Maksimovic, Vladeta Jovovic, Jan 21 2005

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..50

Cf. A006024, A102580 (connected), A102596 (oriented), A102598, A369283.

\\ permcount, edges defined in A369283.
a(n) = {my(s=0); forpart(p=n, s += permcount(p)*(-1)^(n-#p)*edges(p, w->1 + 3^w)); s} \\ Andrew Howroyd, Jan 20 2024

a(n) = Sum_{k>=0} 3^k * A369283(n,k). - Andrew Howroyd, Jan 20 2024

a(0)=1 prepended and a(12) onwards from Andrew Howroyd, Jan 20 2024

A102596 Number of n-node labeled oriented graphs whose underlying graphs are mating graphs, cf. A006024.

Original entry on oeis.org

1, 1, 2, 14, 396, 34748, 9281784, 7454765736, 17754713559696, 124916711439302928, 2595833697671445752352, 159598823327470451154007008, 29105164897431888477084463394496, 15784299558159474546700473641953798080, 25515085085573055700779453120708128026732416

Offset: 0

Goran Kilibarda, Zoran Maksimovic, Vladeta Jovovic, Jan 22 2005

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..50

Cf. A006024, A102579 (digraphs), A102597 (connected), A102599, A369283.

\\ permcount, edges defined in A369283.
a(n) = {my(s=0); forpart(p=n, s += permcount(p)*(-1)^(n-#p)*edges(p, w->1 + 2^w)); s} \\ Andrew Howroyd, Jan 20 2024

a(n) = Sum_{k>=0} 2^k * A369283(n,k). - Andrew Howroyd, Jan 20 2024

a(0)=1 prepended and a(13) onwards from Andrew Howroyd, Jan 20 2024

A102580 Number of n-node labeled connected digraphs whose underlying graphs are mating graphs, cf. A006024.

Original entry on oeis.org

1, 1, 3, 27, 2025, 566190, 625831920, 2774192113350, 49208948146347570, 3472093007861482740960, 971461407155771477392032600, 1076446082528185671934674675023160, 4723701978908086606944984284949329285400, 82155133922723780601138029235949809990647219040

Offset: 0

Goran Kilibarda, Zoran Maksimovic, Vladeta Jovovic, Jan 21 2005

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..50

Cf. A006024, A102579 (not necessarily connected), A102597 (oriented), A102598 (unlabeled), A369283.

\\ b(n) is A102579(n); permcount, edges defined in A369283.
b(n) = {my(s=0); forpart(p=n, s += permcount(p)*(-1)^(n-#p)*edges(p, w->1 + 3^w)); s}
seq(n) = {Vec(serlaplace(1 + x + log(sum(k=0, n, b(k)*x^k/k!, O(x*x^n))/(1 + x))))} \\ Andrew Howroyd, Jan 20 2024

E.g.f.: 1 + x + log(B(x)/(1 + x)) where B(x) is the e.g.f. of A102579. - Andrew Howroyd, Jan 20 2024

a(0)=1 prepended and a(12) onwards from Andrew Howroyd, Jan 20 2024

A102597 Number of n-node labeled connected oriented graphs whose underlying graphs are mating graphs, cf. A006024.

Original entry on oeis.org

1, 1, 2, 8, 352, 32768, 9072896, 7389698048, 17695056717824, 124756911516516352, 2594584522679818518528, 159570269132472101976145920, 29103249711329178773313159168000, 15783921191009840333055992641622114304, 25514864105378775907711095288995558725779456

Offset: 0

Goran Kilibarda, Zoran Maksimovic, Vladeta Jovovic, Jan 22 2005

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..50

Cf. A006024, A102580 (digraphs), A102596 (not necessarily connected), A102599 (unlabeled), A369283.

\\ b(n) is A102596(n); permcount, edges defined in A369283.
b(n) = {my(s=0); forpart(p=n, s += permcount(p)*(-1)^(n-#p)*edges(p, w->1 + 2^w)); s}
seq(n) = {Vec(serlaplace(1 + x + log(sum(k=0, n, b(k)*x^k/k!, O(x*x^n))/(1 + x))))} \\ Andrew Howroyd, Jan 20 2024

E.g.f.: 1 + x + log(B(x)/(1 + x)) where B(x) is the e.g.f. of A102596. - Andrew Howroyd, Jan 20 2024

a(0)=1 prepended and a(13) onwards from Andrew Howroyd, Jan 20 2024

A368987 Triangle read by rows: T(n,k) is the number of unlabeled point-determining graphs with n nodes and k edges, n >= 0, 0 <= k <= n*(n - 1)/2.

Original entry on oeis.org

1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 1, 3, 3, 4, 2, 1, 0, 1, 0, 0, 0, 1, 3, 6, 11, 14, 13, 12, 9, 5, 2, 1, 0, 1, 0, 0, 0, 1, 1, 5, 15, 31, 50, 77, 89, 94, 83, 61, 37, 24, 11, 5, 2, 1, 0, 1, 0, 0, 0, 0, 1, 3, 11, 35, 89, 197, 371, 603, 861, 1068, 1154, 1098, 926, 679, 445, 257, 134, 65, 30, 11, 5, 2, 1, 0, 1

Offset: 0

Andrew Howroyd, Jan 15 2024

Point-determining graphs are also called mating graphs.

			Triangle begins:
[0] 1;
[1] 1;
[2] 0, 1;
[3] 0, 1, 0, 1;
[4] 0, 0, 1, 2, 1, 0,  1;
[5] 0, 0, 1, 1, 3, 3,  4,  2,  1,  0,  1;
[6] 0, 0, 0, 1, 3, 6, 11, 14, 13, 12,  9,  5,  2,  1,  0,  1;
[7] 0, 0, 0, 1, 1, 5, 15, 31, 50, 77, 89, 94, 83, 61, 37, 24, 11, 5, 2, 1, 0, 1;

Andrew Howroyd, Table of n, a(n) for n = 0..175 (rows 0..10)
Ira M. Gessel and Ji Li, Enumeration of point-determining graphs, J. Combinatorial Theory Ser. A 118 (2011), 591-612.

Row sums are A004110.

Cf. A123551 (same row sums), A369283 (labeled).

cp's OEIS Frontend

A102579 Number of n-node labeled digraphs whose underlying graphs are mating graphs, cf. A006024.

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A102596 Number of n-node labeled oriented graphs whose underlying graphs are mating graphs, cf. A006024.

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A102580 Number of n-node labeled connected digraphs whose underlying graphs are mating graphs, cf. A006024.

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A102597 Number of n-node labeled connected oriented graphs whose underlying graphs are mating graphs, cf. A006024.

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A368987 Triangle read by rows: T(n,k) is the number of unlabeled point-determining graphs with n nodes and k edges, n >= 0, 0 <= k <= n*(n - 1)/2.

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