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.

A289170 Number of dominating sets in the n X n white bishop graph.

Original entry on oeis.org

3, 11, 201, 3413, 233727, 15544607, 4103802933, 1069035156713, 1107896230202475, 1142044772648964275, 4697484584102406799521, 19284763179499969013836925, 316392839278535985537956881623, 5187559573137612606140331666573383
Offset: 2

Views

Author

Eric W. Weisstein, Jun 26 2017

Keywords

Crossrefs

Programs

  • PARI
    Collect(sig,v,r,x)={forstep(r=r, 1, -1, my(w=sig[r]+1); v=vector(#v, k, sum(j=1, k, binomial(#v-j,k-j)*v[j]*x^(k-j)*(1+x)^(w-#v+j-1))-v[k])); v[#v]}
    DomSetCount(sig,x)={my(v=[1]); my(total=Collect(sig,v,#sig,x)); forstep(r=#sig, 1, -1, my(w=sig[r]+1); total+=Collect(sig, vector(w,k,if(k<=#v,v[k])), r-1, x); v=vector(w, k, sum(j=1, min(k,#v), binomial(w-j, k-j)*v[j]*x^(k-j)*(1+x)^(j-1)))); total}
    Bishop(n, white)=vector(n-if(white, n%2, 1-n%2), i, n-i+if(white, 1-i%2, i%2));
    a(n)=DomSetCount(Bishop(n,1),1); \\ Andrew Howroyd, Nov 05 2017

Extensions

Terms a(8) and beyond from Andrew Howroyd, Nov 05 2017

A286886 Number of minimal dominating sets in the n X n black bishop graph.

Original entry on oeis.org

1, 2, 5, 19, 84, 425, 2725, 18167, 147458, 1238979
Offset: 1

Views

Author

Eric W. Weisstein, Aug 02 2017

Keywords

Crossrefs

Extensions

a(7) from Eric W. Weisstein, Nov 29 2017
a(8)-a(10) from Andrew Howroyd, Nov 30 2017

A303229 Number of minimal total dominating sets in the n X n white bishop graph.

Original entry on oeis.org

1, 4, 15, 72, 695, 5424, 66861, 721752
Offset: 2

Views

Author

Eric W. Weisstein, Apr 20 2018

Keywords

Crossrefs

Cf. A303230 (black bishop), A321674.

Extensions

a(7)-a(9) from Andrew Howroyd, Apr 20 2018

A323501 Number of minimum dominating sets in the n X n white bishop graph.

Original entry on oeis.org

2, 6, 5, 2, 22, 356, 108, 24, 672, 25056, 4680, 720, 38160, 2531520, 342720, 40320, 3467520, 358444800, 38102400, 3628800, 460857600, 68388364800, 5987520000, 479001600, 84304281600, 16979648716800, 1264085222400, 87178291200, 20312541849600
Offset: 2

Views

Author

Eric W. Weisstein, Jan 16 2019

Keywords

Crossrefs

Cf. A182333 (bishop graph), A323500 (black bishop graph).

Programs

  • Mathematica
    Table[Piecewise[{{(n/2)! (n + 1)/2, Mod[n, 4] == 0}, {((n - 1)/2)!, Mod[n, 4] == 1}, {(n/2 - 1)! (n^2 + n + 2)/4, Mod[n, 4] == 2}, {((n - 3)/2)! (n + 1) (n^3 + n^2 - 6 n + 6)/16, Mod[n, 4] == 3}}], {n, 2, 20}] (* Eric W. Weisstein, Feb 27 2025 *)
  • PARI
    \\ See A289170 for DomSetCount, Bishop.
    a(n)={Vec(DomSetCount(Bishop(n, 1), x + O(x^((n+3)\2))))[1]} \\ Andrew Howroyd, Sep 08 2019
    
  • PARI
    a(n)=(n\4*2)!*if(n%4<2, if(n%2==0, (n + 1)/2, 1), if(n%2==0, (n^2 + n + 2)/4, (n + 1)*(n^3 + n^2 - 6*n + 6)/16)); \\ Andrew Howroyd, Sep 09 2019

Formula

From Andrew Howroyd, Sep 09 2019: (Start)
a(n) = (n/2)! * (n + 1)/2 for n mod 4 = 0;
a(n) = ((n-1)/2)! for n mod 4 = 1;
a(n) = (n/2-1)! * (n^2 + n + 2)/4 for n mod 4 = 2;
a(n) = ((n-3)/2)! * (n + 1)*(n^3 + n^2 - 6*n + 6)/16 for n mod 4 = 3.
(End)

Extensions

Offset corrected and terms a(11) and beyond from Andrew Howroyd, Sep 08 2019

A295899 Number of minimal dominating sets in the n X n bishop graph.

Original entry on oeis.org

1, 4, 30, 361, 6552, 180625, 6768900, 330039889, 20267217352, 1535068962441
Offset: 1

Views

Author

Eric W. Weisstein, Nov 29 2017

Keywords

Crossrefs

Formula

a(n) = A286886(n) * A287897(n). - Andrew Howroyd, Nov 30 2017

Extensions

a(6)-a(10) from Andrew Howroyd, Nov 30 2017
Showing 1-5 of 5 results.