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Search: a057279 -id:a057279
Displaying 1-5 of 5 results found. page 1
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A057270 Triangle T(n,k) of number of unilaterally connected digraphs on n unlabeled nodes with k arcs, k=0..n*(n-1). +0
7
1, 0, 1, 1, 0, 0, 1, 4, 4, 1, 1, 0, 0, 0, 1, 10, 30, 45, 38, 27, 13, 5, 1, 1, 0, 0, 0, 0, 1, 20, 136, 462, 972, 1412, 1639, 1485, 1152, 707, 379, 154, 61, 16, 5, 1, 1, 0, 0, 0, 0, 0, 1, 35, 437, 2833, 11325, 31615, 67207, 115344, 165762, 204723, 219866, 206986, 170920, 124088, 78809, 43860, 21209, 8951, 3242, 1043, 288, 76, 17, 5, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,8
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973.
LINKS
Table of n, a(n) for n=1..76.
R. W. Robinson, Counting strong digraphs (research announcement), J. Graph Theory 1, 1977, pp. 189-190.
EXAMPLE
[1],[0,1,1],[0,0,1,4,4,1,1],[0,0,0,1,10,30,45,38,27,13,5,1,1],...; Number of unilaterally connected digraphs on 4 unlabeled nodes is 171=1+10+30+45+38+27+13+5+1+1.
CROSSREFS
Row sums give A003088. Cf. A057271-A057279.
KEYWORD
nonn,tabf
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Aug 23 2000
EXTENSIONS
More terms from Sean A. Irvine, May 27 2022
STATUS
approved
A057272 Triangle T(n,k) of number of digraphs with a quasi-source on n labeled nodes and with k arcs, k=0,1,..,n*(n-1). +0
5
1, 0, 2, 1, 0, 0, 12, 20, 15, 6, 1, 0, 0, 0, 104, 426, 768, 920, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 1160, 9184, 32420, 73000, 123425, 166860, 184426, 167900, 125965, 77520, 38760, 15504, 4845, 1140, 190, 20, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Table of n, a(n) for n=1..45.
V. Jovovic and G. Kilibarda, Enumeration of labeled quasi-initially connected digraphs, Discrete Math., 224 (2000), 151-163.
EXAMPLE
Triangle starts:
1;
0,2,1;
0,0,12,20,15,6,1;
0,0,0,104,426,768,920,792,495,220,66,12,1;
...
Number of digraphs with a quasi-source on 3 labeled nodes is 54=12+20+15+6+1.
CROSSREFS
Row sums give A049414. Cf. A057270, A057271, A057273-A057279.
KEYWORD
nonn,tabf
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Sep 14 2000
STATUS
approved
A057276 Triangle T(n,k) of number of strongly connected digraphs on n unlabeled nodes and with k arcs, k=0..n*(n-1). +0
10
1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 0, 1, 4, 16, 22, 22, 11, 5, 1, 1, 0, 0, 0, 0, 0, 1, 7, 58, 240, 565, 928, 1065, 953, 640, 359, 150, 59, 16, 5, 1, 1, 0, 0, 0, 0, 0, 0, 1, 10, 165, 1281, 6063, 19591, 47049, 87690, 131927, 163632, 170720, 151238, 115122, 75357, 42745, 20891, 8877, 3224, 1039, 286, 76, 17, 5, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..2680 (rows 1..20)
EXAMPLE
Triangle begins:
[1] 1;
[2] 0,0,1;
[3] 0,0,0,1,2,1,1;
[4] 0,0,0,0,1,4,16,22,22,11,5,1,1;
...
The number of strongly connected digraphs on 3 unlabeled nodes is 5 = 1+2+1+1.
PROG
(PARI) \\ See PARI link in A350489 for program code.
{ my(A=A057276rows(5)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 13 2022
CROSSREFS
Row sums give A035512.
Column sums give A350752.
The labeled version is A057273.
Cf. A054733, A057270, A057277, A057278, A057279, A350489.
KEYWORD
nonn,tabf
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Sep 14 2000
EXTENSIONS
Terms a(46) and beyond from Andrew Howroyd, Jan 13 2022
STATUS
approved
A057277 Triangle T(n,k) of number of digraphs with a source on n unlabeled nodes with k arcs, k=0..n*(n-1). +0
8
1, 0, 1, 1, 0, 0, 2, 4, 4, 1, 1, 0, 0, 0, 4, 16, 34, 46, 38, 27, 13, 5, 1, 1, 0, 0, 0, 0, 9, 56, 229, 573, 1058, 1448, 1653, 1487, 1153, 707, 379, 154, 61, 16, 5, 1, 1, 0, 0, 0, 0, 0, 20, 198, 1218, 5089, 15596, 37302, 72776, 119531, 168233, 205923, 220337, 207147, 170965, 124099, 78811, 43861, 21209, 8951, 3242, 1043, 288, 76, 17, 5, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,7
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..2680 (rows 1..20)
EXAMPLE
Triangle begins:
[1],
[0, 1, 1],
[0, 0, 2, 4, 4, 1, 1],
[0, 0, 0, 4, 16, 34, 46, 38, 27, 13, 5, 1, 1],
....
The number of digraphs with a source on 3 unlabeled nodes is 12 = 2+4+4+1+1.
PROG
(PARI) \\ See PARI link in A350794 for program code.
{ my(A=A057277triang(5)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 21 2022
CROSSREFS
Row sums give A051421.
Column sums give A350907.
The labeled version is A057274.
Cf. A057270, A057276, A057278, A057279, A350794, A350797.
KEYWORD
nonn,tabf
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Sep 14 2000
EXTENSIONS
Terms a(46) and beyond from Andrew Howroyd, Jan 21 2022
STATUS
approved
A057278 Triangle T(n,k) of number of digraphs with a source and a sink on n unlabeled nodes and k arcs, k=0..n*(n-1). +0
9
1, 0, 1, 1, 0, 0, 1, 4, 4, 1, 1, 0, 0, 0, 1, 11, 31, 45, 38, 27, 13, 5, 1, 1, 0, 0, 0, 0, 1, 23, 152, 486, 992, 1419, 1641, 1485, 1152, 707, 379, 154, 61, 16, 5, 1, 1, 0, 0, 0, 0, 0, 1, 42, 517, 3194, 12174, 32860, 68423, 116168, 166164, 204867, 219906, 206993, 170922, 124088, 78809, 43860, 21209, 8951, 3242, 1043, 288, 76, 17, 5, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,8
REFERENCES
V. Jovovic, G. Kilibarda, Enumeration of labeled initially-finally connected digraphs, Scientific review, Serbian Scientific Society, 19-20 (1996), p. 246.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..2680 (rows 1..20)
EXAMPLE
Triangle begins:
[1],
[0,1,1],
[0,0,1,4,4,1,1],
[0,0,0,1,11,31,45,38,27,13,5,1,1],
...
The number of digraphs with a source and a sink on 3 unlabeled nodes is 11 = 1+4+4+1+1.
PROG
(PARI) \\ See PARI link in A350794 for program code.
{ my(A=A057278triang(5)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 21 2022
CROSSREFS
Row sums give A049531.
Column sums give A350906.
The labeled version is A057271.
Cf. A057270, A057276, A057277, A057279, A350794, A350795.
KEYWORD
nonn,tabf
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Sep 14 2000
EXTENSIONS
Terms a(46) and beyond from Andrew Howroyd, Jan 21 2022
STATUS
approved
page 1

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Last modified August 30 15:13 EDT 2024. Contains 375545 sequences. (Running on oeis4.)