cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A006787 Number of n-node graphs with no cycles of length less than 5.

Original entry on oeis.org

1, 2, 3, 6, 11, 23, 48, 114, 293, 869, 2963, 12066, 58933, 347498, 2455693, 20592932, 202724920, 2322206466, 30743624324, 468026657815, 8161170076257
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Includes graphs with no cycles at all as well as graphs with girth greater than 5.

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A000066, A000088, A054760, A159847, A126757 (connected, inv. Eul. Transf.), A128236, A128237, A300705.

Formula

a(n) = A000088(n) - A128236(n) - A128237(n). - Andrew Howroyd, May 06 2021

Extensions

Definition corrected by Brendan McKay, Apr 27 2007
a(18)-a(19) (from the McKay reference) added by R. J. Mathar, Jun 17 2008
a(20)-a(21) from Brendan McKay, Mar 11 2018

A140440 Number of n-node biconnected graphs with girth at least 5.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 2, 5, 12, 40, 154, 766, 4672, 34547, 302185, 3073267, 35933851, 479768761, 7284446498, 125435333136
Offset: 1

Views

Author

Brendan McKay, Jun 17 2008

Keywords

Examples

			The 5 graphs of order 8 are:
0: 4 6; 1: 5 6; 2: 5 7; 3: 6 7; 4: 0 7; 5: 1 2; 6: 0 1 3; 7: 2 3 4;
0: 4 5; 1: 4 6; 2: 5 7; 3: 6 7; 4: 0 1; 5: 0 2; 6: 1 3; 7: 2 3;
0: 4 5; 1: 4 6; 2: 5 7; 3: 6 7; 4: 0 1 7; 5: 0 2; 6: 1 3; 7: 2 3 4;
0: 4 5; 1: 4 7; 2: 5 6; 3: 6 7; 4: 0 1 6; 5: 0 2 7; 6: 2 3 4; 7: 1 3 5;
0: 3 6; 1: 4 6; 2: 5 6; 3: 0 7; 4: 1 7; 5: 2 7; 6: 0 1 2; 7: 3 4 5.

Crossrefs

Cf. A126757.

Extensions

a(18)-a(20) from Brendan McKay, Jun 13 2021

A128241 Number of n-node (unlabeled) connected graphs with girth 4.

Original entry on oeis.org

0, 1, 2, 11, 41, 220, 1243, 9368, 89049, 1135894, 19381407, 445505570, 13741579905, 566739127723, 31124921885829
Offset: 3

Views

Author

Keith Briggs, May 05 2007

Keywords

Crossrefs

Cf. A024607, A126757.
Cf. A128041, A128042, A128236-A128243.

Formula

a(n) = A024607(n) - A126757(n). - Martin Fuller, May 01 2015

Extensions

Corrected and extended by Martin Fuller, May 01 2015

A300705 Triangle T(n,k) read by rows: the number of n-node connected graphs with k components with no cycles of length less than 5.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 4, 3, 2, 1, 1, 0, 8, 7, 4, 2, 1, 1, 0, 18, 14, 8, 4, 2, 1, 1, 0, 47, 33, 17, 9, 4, 2, 1, 1, 0, 137, 81, 40, 18, 9, 4, 2, 1, 1, 0, 464, 228, 98, 43, 19, 9, 4, 2, 1, 1, 0, 1793, 716, 269, 105, 44, 19, 9, 4, 2, 1, 1, 0, 8167, 2596, 827, 287, 108, 45, 19, 9, 4, 2, 1, 1, 0
Offset: 0

Views

Author

R. J. Mathar, Mar 12 2018

Keywords

Comments

Multiset transform of A126757.

Examples

			The triangle starts in row n=0 with columns 0<=k<=n as:
 1;
0 1
0 1 1
0 1 1 1
0 2 2 1 1
0 4 3 2 1 1
0 8 7 4 2 1 1
0 18 14 8 4 2 1 1
0 47 33 17 9 4 2 1 1
0 137 81 40 18 9 4 2 1 1
0 464 228 98 43 19 9 4 2 1 1
0 1793 716 269 105 44 19 9 4 2 1 1
0 8167 2596 827 287 108 45 19 9 4 2 1 1
0 43645 11030 2904 870 294 109 45 19 9 4 2 1 1
0 275480 55628 11992 3022 888 297 110 45 19 9 4 2 1 1
0 2045279 334676 58968 12320 3066 895 298 110 45 19 9 4 2 1 1
0 17772647 2395216 348166 59991 12440 3084 898 299 110 45 19 9 4 2 1 1

Crossrefs

Cf. A126757 (column k=1), A006787 (row sums)
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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