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.

A303334 Number of dominating sets in the n X n torus grid graph.

Original entry on oeis.org

421, 45707, 18935741, 30147126791, 183429997068809, 4264383011657313355, 378801055723829891830261, 128572687866388429165521180651, 166751578049943666873090557914876017, 826369316231187306403443156508234313658719, 15648091232010974513543383340423707992718009437149
Offset: 3

Views

Author

Andrew Howroyd, Apr 21 2018

Keywords

Links

Crossrefs

Cf. A295428, A298106, A303210.

Extensions

a(9) and beyond from Stephan Mertens, Aug 18 2024

A302406 Total domination number of the n X n torus grid graph.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 10, 14, 16, 23, 26, 33, 36, 46, 50, 60, 64, 77, 82, 95, 100, 116, 122, 138, 144, 163, 170, 189, 196, 218, 226, 248, 256, 281, 290, 315, 324, 352, 362, 390, 400, 431, 442, 473, 484, 518, 530, 564, 576, 613, 626, 663, 676, 716, 730, 770, 784, 827, 842, 885
Offset: 0

Views

Author

Eric W. Weisstein, Apr 07 2018

Keywords

Comments

Extended to a(0)-a(2) using the formula/recurrence.

Links

Crossrefs

Cf. A303210, A303213.

Programs

  • Magma
    R:=RealField(); [Round((3 -(-1)^n*(n-1) +n +2*n^2 - 4*Cos(n*Pi(R)/2) + 2*Sin(n*Pi(R)/2))/8): n in [0..20]]; // G. C. Greubel, Apr 09 2018
  • Mathematica
    Table[(3-(-1)^n*(n-1)+n+2*n^2-4*Cos[n*Pi/2]+2*Sin[n*Pi/2])/8, {n, 0, 20}]
LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {1, 2, 3, 4, 8, 10, 14}, {0, 20}]
CoefficientList[Series[-x (1 + x + 2 x^4)/((-1 + x)^3 (1 + x)^2 (1 + x^2)), {x, 0, 20}], x]
  • PARI
    for(n=0,30, print1(round((3-(-1)^n*(n-1) +n +2*n^2 -4*cos(n*Pi/2) + 2*sin(n*Pi/2))/8), ", ")) \\ G. C. Greubel, Apr 09 2018

Formula

a(n) = (3 -(-1)^n*(n - 1) + n + 2*n^2 - 4*cos(n*Pi/2) + 2*sin(n*Pi/2))/8.
a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7).
G.f.: -x*(1 + x + 2*x^4)/((-1 + x)^3*(1 + x)^2*(1 + x^2)).
a(n) ~ n^2/4. - Andrew Howroyd, Apr 21 2018

A303213 Number of minimum total dominating sets in the n X n torus grid graph.

Original entry on oeis.org

6, 16, 400, 324, 28, 144, 7452, 2500, 44, 784
Offset: 3

Views

Author

Eric W. Weisstein, Apr 19 2018

Keywords

Links

Crossrefs

Cf. A302406, A303210.

Extensions

a(6)-a(8) from Andrew Howroyd, Apr 21 2018
a(9)-a(10) from Eric W. Weisstein, Mar 31 2025
a(11)-a(12) from Eric W. Weisstein, Apr 04 2025
Showing 1-3 of 3 results.

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

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