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 1-7 of 7 results.

A286209 Number of n X 1 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 3, 10, 24, 60, 134, 304, 656, 1420, 2996, 6312, 13112, 27167, 55825, 114412, 233282, 474563, 962159, 1947098, 3931288, 7925708, 15952866, 32072580, 64404708, 129213082, 259009006, 518818124, 1038549912, 2077775396, 4154785904, 8304424080
Offset: 0

Views

Author

R. H. Hardin, May 04 2017

Keywords

Examples

			All solutions for n=7
..0. .0. .0
..1. .0. .1
..0. .1. .0
..0. .0. .0
..0. .0. .1
..1. .1. .0
..0. .0. .0

Links

Crossrefs

Column k=1 of A286216.
Column k=2 of A307796.

Programs

  • Maple
    b:= proc(n, t, h, c) option remember; `if`(abs(c-2)>n, 0, `if`(n=0, 1,
      b(n-1, [1, 3, 1][t], 2, c-`if`(h=3, 1, 0))+
      b(n-1, 2, [1, 3, 1][h], c+`if`(t=3, 1, 0))))
    end:
a:= n-> b(n, 1$2, 0):
seq(a(n), n=0..40);  # Alois P. Heinz, Apr 29 2019
  • Mathematica
    b[n_, t_, h_, c_] := b[n, t, h, c] = If[Abs[c - 2] > n, 0, If[n == 0, 1,
     b[n - 1, {1, 3, 1}[[t]], 2, c - If[h == 3, 1, 0]] +
     b[n - 1, 2, {1, 3, 1}[[h]], c + If[t == 3, 1, 0]]]];
a[n_] := b[n, 1, 1, 0];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 27 2022, after Alois P. Heinz *)

A286210 Number of n X 2 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1.

Original entry on oeis.org

0, 4, 17, 62, 238, 912, 3468, 13224, 50655, 194672, 750165, 2897898, 11219322, 43520672, 169113746, 658172740, 2565143148, 10010037116, 39107620002, 152948221004, 598750691827, 2346021879720, 9199672561659, 36102743330922
Offset: 1

Views

Author

R. H. Hardin, May 04 2017

Keywords

Comments

Column 2 of A286216.

Examples

			Some solutions for n=4
..1..0. .0..1. .1..0. .0..0. .0..0. .0..0. .1..0. .0..1. .0..1. .0..0
..0..0. .0..0. .0..1. .0..0. .0..1. .1..1. .1..0. .0..0. .0..1. .0..1
..0..1. .0..1. .0..0. .0..0. .0..1. .0..0. .0..1. .1..0. .1..0. .0..1
..0..1. .1..0. .0..1. .0..1. .1..0. .1..0. .0..0. .0..1. .0..0. .0..1

Links

Crossrefs

Cf. A286216.

A286211 Number of n X 3 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1.

Original entry on oeis.org

0, 17, 52, 684, 2128, 34896, 123541, 1891998, 7565509, 106100847, 470286934, 6070072444, 29342743563, 352400491431, 1833102380708, 20699165970978, 114576111229319, 1227555854005393, 7163217232141967, 73387852919316000
Offset: 1

Views

Author

R. H. Hardin, May 04 2017

Keywords

Comments

Column 3 of A286216.

Examples

			Some solutions for n=4
..1..0..0. .1..0..1. .0..1..1. .1..0..0. .1..1..0. .0..1..0. .0..0..1
..0..1..0. .0..0..1. .1..0..0. .1..0..0. .1..0..0. .0..1..0. .0..0..0
..0..1..1. .0..0..0. .1..0..0. .0..0..0. .0..0..0. .1..1..0. .0..0..1
..0..0..1. .0..1..1. .0..1..0. .1..0..1. .1..0..0. .1..0..0. .1..1..0

Links

Crossrefs

Cf. A286216.

A286212 Number of n X 4 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1.

Original entry on oeis.org

0, 62, 684, 10056, 141018, 2053994, 30004158, 443275636, 6591532114, 98620717026, 1483077002788, 22402256622648, 339716751362128, 5169528508115318, 78910865975553660, 1207934007828690708, 18537787151292561428
Offset: 1

Views

Author

R. H. Hardin, May 04 2017

Keywords

Comments

Column 4 of A286216.

Examples

			Some solutions for n=4
..0..0..0..1. .1..0..1..0. .0..1..0..1. .1..0..0..0. .0..1..0..1
..1..1..0..0. .1..0..0..0. .0..0..1..1. .1..0..1..0. .0..1..0..0
..1..1..0..0. .0..0..1..0. .0..1..1..0. .0..0..0..1. .1..0..0..1
..1..0..1..0. .1..1..1..0. .1..0..0..0. .1..1..0..1. .1..1..0..0

Links

Crossrefs

Cf. A286216.

A286213 Number of n X 5 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1.

Original entry on oeis.org

0, 238, 2128, 141018, 1656022, 113258929, 1569283128, 97311031516, 1540259241508, 86480812173044, 1526208889551285, 78586854206474282, 1517934653629840928, 72607979076706778162, 1512452308916246272882
Offset: 1

Views

Author

R. H. Hardin, May 04 2017

Keywords

Comments

Column 5 of A286216.

Examples

			Some solutions for n=4
..0..0..1..0..0. .0..0..0..1..0. .0..1..1..0..1. .0..0..0..1..1
..0..0..1..0..1. .0..1..0..0..0. .0..0..1..0..1. .0..1..1..1..1
..0..0..0..0..1. .0..1..1..0..1. .0..0..0..1..0. .1..0..1..0..0
..1..0..1..1..1. .1..1..1..0..1. .0..0..1..0..1. .0..0..1..0..0

Links

Crossrefs

Cf. A286216.

A286214 Number of n X 6 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1.

Original entry on oeis.org

1, 912, 34896, 2053994, 113258929, 6553131164, 380797680269, 22418184755710, 1330080388106827, 79466576915681740, 4775393278095153395, 288397740505442452180, 17492553727454266741242, 1065040889415828916901252
Offset: 1

Views

Author

R. H. Hardin, May 04 2017

Keywords

Comments

Column 6 of A286216.

Examples

			Some solutions for n=3
..1..0..0..1..0..0. .0..0..1..1..1..1. .1..1..0..0..1..0. .1..0..1..1..0..0
..1..1..0..0..1..0. .0..1..0..0..0..0. .0..1..1..0..0..0. .1..0..0..0..1..1
..0..1..1..0..0..1. .0..1..0..0..1..1. .0..1..0..0..1..1. .0..1..0..0..0..1

Links

Crossrefs

Cf. A286216.

A286215 Number of n X 7 0..1 arrays with the number of 1's king-move adjacent to some 0 two less than the number of 0's adjacent to some 1.

Original entry on oeis.org

3, 3468, 123541, 30004158, 1569283128, 380797680269, 23594688741164, 5201563721481604, 366234192215237315, 73710966822498902306, 5745557094114966956143, 1070211615398838835193976
Offset: 1

Views

Author

R. H. Hardin, May 04 2017

Keywords

Comments

Column 7 of A286216.

Examples

			Some solutions for n=3
..0..1..0..0..0..1..1. .1..1..0..0..0..0..1. .0..0..1..1..0..0..0
..1..0..0..0..1..0..0. .0..1..1..0..0..1..1. .1..1..1..0..0..0..1
..1..1..0..1..1..0..0. .0..0..0..1..0..1..1. .1..1..0..0..1..1..0

Links

Crossrefs

Cf. A286216.
Showing 1-7 of 7 results.

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