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 1-3 of 3 results.

A103300 Number of perfect rulers with length n.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 2, 12, 8, 4, 38, 30, 14, 6, 130, 80, 32, 12, 500, 326, 150, 66, 18, 4, 944, 460, 166, 56, 12, 6, 2036, 890, 304, 120, 20, 10, 2, 2678, 974, 362, 100, 36, 4, 2, 4892, 2114, 684, 238, 68, 22, 4, 16318, 6350, 2286, 836, 330, 108, 24, 12, 31980, 12252
Offset: 0

Views

Author

Peter Luschny, Feb 28 2005

Keywords

Comments

For definitions, references and links related to complete rulers see A103294.
The values for n = 208-213 are 22,0,0,0,4,4 according to Arch D. Robison. The values for 199-207 are not yet known. - Peter Luschny, Feb 20 2014, Jun 28 2019
Zero values at 135, 136, 149, 150, 151, 164, 165, 166, 179, 180, 181, 195, 196, 209, 210, 211. - Ed Pegg Jr, Jun 23 2019 [These values were found by Arch D. Robison, see links. Peter Luschny, Jun 28 2019]
From Yannic Schröder, Feb 22 2021: (Start)
Zero values at 135, 136, 149, 150, 151, 164, 165, 166, 179, 180, 181, 195, 196 have been replaced with correct values using an additional mark.
A lower bound for 209 is 62, for 210 is 16, and for 211 is 204.
The verified value for 212 and for 213 is 4. (End)

Examples

			a(5)=4 counts the perfect rulers with length 5, {[0,1,3,5],[0,2,4,5],[0,1,2,5],[0,3,4,5]}.

Links

Crossrefs

Cf. A004137 (Maximal number of edges in a graceful graph on n nodes).
Cf. A103301, A103297, A103298.

Formula

a(n) = T(n, A103298(n)) where the triangle T is described by A103294.

A103298 Number of segments of a perfect ruler with length n.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14
Offset: 0

Views

Author

Peter Luschny, Feb 28 2005

Keywords

Comments

For definitions, references and links related to complete rulers see A103294.

Examples

			a(11)=5 means that a perfect ruler with length 11 has 5 segments.

Links

Crossrefs

Cf. A046693, A103297.

Formula

a(n) = A046693(n) - 1.

Extensions

Extended using A046693 terms by Vaclav Kotesovec, Oct 20 2019

A103301 Number of perfect rulers with n segments (n>=0).

Original entry on oeis.org

1, 1, 3, 9, 24, 88, 254, 1064, 1644, 3382, 4156, 8022, 26264, 52012, 25434, 8506, 5632, 6224, 12330, 34224, 108854, 103156, 75992, 86560, 69084
Offset: 0

Views

Author

Peter Luschny, Feb 28 2005

Keywords

Comments

For definitions, references and links related to complete rulers see A103294.

Examples

			a(3)=9 counts the perfect rulers with 3 segments, {[0,1,2,4],[0,2,3,4], [0,1,3,4],[0,1,3,5],[0,2,4,5],[0,1,2,5],[0,3,4,5],[0,1,4,6],[0,2,5,6]}.

Links

Crossrefs

Cf. A103300, A103297, A103296 (Complete rulers with n segments), A103299 (Optimal rulers with n segments).

Formula

a(n) = Sum_{i=A004137(n)+1..A004137(n+1)} A103300(i), n>=1.

Extensions

Terms a(19)-a(24) found by exhaustive search by Fabian Schwartau, Yannic Schröder, Lars Wolf, Joerg Schoebel, Feb 23 2021
Showing 1-3 of 3 results.

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

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