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 1-2 of 2 results.

A347633 Number of minimum dominating sets in the path graph P_n.

Original entry on oeis.org

1, 2, 1, 4, 3, 1, 8, 4, 1, 13, 5, 1, 19, 6, 1, 26, 7, 1, 34, 8, 1, 43, 9, 1, 53, 10, 1, 64, 11, 1, 76, 12, 1, 89, 13, 1, 103, 14, 1, 118, 15, 1, 134, 16, 1, 151, 17, 1, 169, 18, 1, 188, 19, 1, 208, 20, 1, 229, 21, 1, 251, 22, 1, 274, 23, 1, 298, 24, 1, 323
Offset: 1

Views

Author

Eric W. Weisstein, Sep 09 2021

Keywords

Crossrefs

Row 1 of A350815 and A350820.

Programs

  • Mathematica
    Table[Piecewise[{{1, Mod[n, 3] == 0}, {(n^2 + 13 n + 4)/18, Mod[n, 3] == 1}, {(n + 4)/3, Mod[n, 3] == 2}}], {n, 20}]
    LinearRecurrence[{0, 0, 3, 0, 0, -3, 0, 0, 1}, {1, 2, 1, 4, 3, 1, 8, 4, 1}, 20]
    CoefficientList[Series[-(1 + 2 x + x^2 + x^3 - 3 x^4 - 2 x^5 - x^6 + x^7 + x^8)/((-1 + x)^3 (1 + x + x^2)^3), {x, 0, 20}], x]
  • PARI
    a(n)={if(n%3==0, 1, if(n%3==1, (n^2+13*n+4)/18,  (n+4)/3))} \\ Andrew Howroyd, Jan 18 2022

Formula

a(n) = 1 for n = 0 (mod 3)
(n^2+13*n+4)/18 for n = 1 (mod 3)
(n+4)/3 for n = 2 (mod 3).
a(n) = 3*a(n-3)-3*a(n-6)+a(n-9) for n > 9.
G.f.: -(x*(1+2*x+x^2+x^3-3*x^4-2*x^5-x^6+x^7+x^8))/((-1+x)^3*(1+x+x^2)^3).

A375566 Array read by antidiagonals: T(m,n) = number of minimum dominating sets in the stacked prism graph C_m X P_n.

Original entry on oeis.org

1, 2, 2, 1, 6, 3, 4, 3, 9, 6, 3, 12, 34, 4, 5, 1, 2, 123, 4, 10, 3, 8, 17, 3, 16, 5, 51, 14, 4, 2, 18, 28, 290, 18, 14, 8, 1, 20, 93, 76, 320, 6, 63, 4, 3, 13, 2, 438, 164, 265, 171, 14, 4, 18, 25, 5, 24, 3, 396, 255, 36, 91, 24, 9, 120, 11, 1, 2, 27, 904, 250, 6, 1526, 60, 2052, 25, 22, 3
Offset: 1

Views

Author

Stephan Mertens, Aug 19 2024

Keywords

Examples

			Table starts:
====================================
m\n |   1   2   3    4    5    6 ...
----+-------------------------------
  1 |   1   2   1    4    3    1 ...
  2 |   2   6   3   12    2   17 ...
  3 |   3   9  34  123    3   18 ...
  4 |   6   4   4   16   28   76 ...
  5 |   5  10   5  290  320  265 ...
 ...
		

Crossrefs

Main diagonal is A375569.
Rows 1..2 are A347633, A347558.
Column 1 is A347538, column 2 is essentially A347634.
Showing 1-2 of 2 results.