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 1-5 of 5 results.

A287064 Number of dominating sets in the n-triangular grid graph.

Original entry on oeis.org

1, 7, 45, 685, 20409, 1201941, 141147379, 32952001519, 15299378914117, 14127550190798059, 25944752255914338751, 94759724685920514675099, 688318811614248548827285461, 9943676783895971991257124086453, 285690558616920990681823749334591359, 16324365307318944099676240468111164604873
Offset: 0

Views

Author

Eric W. Weisstein, May 19 2017

Keywords

Links

Crossrefs

Cf. A251419, A288721, A297572, A303049.

Extensions

a(7)-a(11) from Andrew Howroyd, May 21 2017
Terms a(12) and beyond from Andrew Howroyd, Apr 18 2018

A302486 Total domination number of the n-triangular grid graph.

Original entry on oeis.org

2, 2, 4, 5, 6, 8, 10, 12, 15, 17, 20, 23, 26, 30, 33, 36, 40, 45, 49, 54, 58, 63, 69, 74
Offset: 1

Views

Author

Eric W. Weisstein, Apr 08 2018

Keywords

Links

Crossrefs

Cf. A251419, A303049.

Formula

a(n) ~ n^2/10. - Andrew Howroyd, May 20 2018

Extensions

a(11)-a(15) from Andrew Howroyd, Apr 18 2018
a(16)-a(17) from Eric W. Weisstein, Apr 18 2018
a(18) from Eric W. Weisstein, Apr 20 2018
a(19) from Andrew Howroyd, May 19 2018
a(20)-a(24) from Eric W. Weisstein, Sep 22-23 2021

A297572 Number of minimum dominating sets in the n-triangular grid graph.

Original entry on oeis.org

1, 3, 6, 26, 2, 75, 89, 18, 108, 4, 9042, 10265, 10524, 138, 8, 72, 596, 4438, 390, 16, 55716
Offset: 0

Views

Author

Eric W. Weisstein, Dec 31 2017

Keywords

Links

Crossrefs

Cf. A251419, A287064, A288721.

Extensions

a(8)-a(10) from Andrew Howroyd, Jan 02 2018
Offset corrected and a(11)-a(20) from Andrew Howroyd, May 19 2018

A251418 Floor((n^2+7n-23)/14).

Original entry on oeis.org

-2, -2, -1, 0, 1, 2, 3, 5, 6, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 36, 40, 43, 47, 51, 55, 59, 63, 68, 72, 77, 82, 87, 92, 97, 103, 108, 114, 120, 126, 132, 138, 145, 151, 158, 165, 172, 179, 186, 194, 201, 209, 217, 225, 233, 241, 250, 258, 267, 276
Offset: 0

Views

Author

N. J. A. Sloane, Dec 04 2014

Keywords

Comments

This is conjectured to be the value of the dominance number of the triangle grid graph for n >= 14 - see A251419.

Links

Crossrefs

Cf. A251419.

Programs

  • Magma
    [Floor((n^2+7*n-23)/14): n in [0..60]]; // Vincenzo Librandi, Dec 04 2014
  • Mathematica
    Table[Floor[(n^2 + 7 n - 23) / 14], {n, 0, 80}] (* Vincenzo Librandi, Dec 04 2014 *)
LinearRecurrence[{2,-1,0,0,0,0,1,-2,1},{-2,-2,-1,0,1,2,3,5,6},60] (* Harvey P. Dale, Mar 19 2020 *)
  • PARI
    Vec((3*x^8-3*x^7-x^2-2*x+2)/((x-1)^3*(x^6+x^5+x^4+x^3+x^2+x+1)) + O(x^100)) \\ Colin Barker, Jul 10 2015

Formula

G.f.: (3*x^8-3*x^7-x^2-2*x+2) / ((x-1)^3*(x^6+x^5+x^4+x^3+x^2+x+1)). - Colin Barker, Jul 10 2015

Extensions

More terms from Vincenzo Librandi, Dec 04 2014

A379353 Connected domination number of the n-triangular grid graph.

Original entry on oeis.org

1, 1, 2, 4, 6, 8, 10, 13, 17, 20, 23, 28, 32, 37, 41, 47, 52
Offset: 0

Views

Author

Andrew Howroyd, Dec 27 2024

Keywords

Links

Crossrefs

Cf. A251419, A288721, A373393.

Formula

a(n) >= floor((n^2 + 3*n + 10)/6) for n >= 3.
a(n) ~ n^2/6.
Showing 1-5 of 5 results.

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

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