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.

A231581 Number of nX2 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

4, 28, 124, 602, 2776, 12922, 60720, 286047, 1335296, 6256326, 29377828, 137595239, 644951590, 3024402309, 14175895645, 66459189937, 311583082104, 1460702584712, 6848241858778, 32106603868468, 150524267596760, 705711781367756
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2013

Keywords

Comments

Column 2 of A231586

Examples

			Some solutions for n=7
..0..0....3..0....2..1....0..3....2..0....2..3....2..2....1..1....3..3....0..0
..0..2....0..0....1..1....0..0....0..0....2..2....0..0....2..1....0..0....0..1
..1..0....0..0....0..0....0..1....1..0....3..2....0..0....1..2....0..0....0..0
..0..0....0..2....0..0....0..2....0..0....1..1....1..3....0..0....0..3....3..0
..2..0....0..1....0..2....0..0....0..1....1..1....0..0....0..0....0..0....0..1
..2..0....0..0....2..0....0..0....0..0....1..1....0..0....0..0....3..0....0..0
..0..0....0..0....0..0....2..0....3..0....2..1....2..3....0..2....0..0....0..3
		

Programs

  • Maple
    rec:= a(n) = 4*a(n-1) +6*a(n-2) +38*a(n-3) -161*a(n-4) -292*a(n-5) -953*a(n-6) +1185*a(n-7) +4928*a(n-8) +12336*a(n-9) +7076*a(n-10) -7076*a(n-11) -24464*a(n-12) -24608*a(n-13) -18624*a(n-14) -6720*a(n-15) -2304*a(n-16):
    Data := [4, 28, 124, 602, 2776, 12922, 60720, 286047, 1335296, 6256326, 29377828, 137595239, 644951590, 3024402309, 14175895645, 66459189937]:
    f:= gfun:-rectoproc({rec,seq(a(i)=Data[i],i=1..16)},a(n),remember):
    map(f, [$1..40]); # Robert Israel, Dec 06 2017

Formula

Empirical: a(n) = 4*a(n-1) +6*a(n-2) +38*a(n-3) -161*a(n-4) -292*a(n-5) -953*a(n-6) +1185*a(n-7) +4928*a(n-8) +12336*a(n-9) +7076*a(n-10) -7076*a(n-11) -24464*a(n-12) -24608*a(n-13) -18624*a(n-14) -6720*a(n-15) -2304*a(n-16).
Empirical formula verified by Robert Israel, Dec 06 2017 (see link).

A231582 Number of nX3 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

16, 124, 2352, 32650, 381076, 5618444, 82479418, 1142396851, 16061107556, 231334122108, 3304782498636, 47013530431780, 672506204379038, 9632530214937964, 137769361857359282, 1971267194035271726
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2013

Keywords

Comments

Column 3 of A231586

Examples

			Some solutions for n=4
..1..0..0....3..0..1....1..0..3....0..2..3....2..2..1....2..3..1....1..1..1
..0..0..3....0..0..0....0..0..0....0..0..2....1..0..0....2..1..1....2..1..1
..0..3..0....0..0..0....3..0..1....0..0..3....0..0..0....0..0..3....3..1..1
..2..0..0....3..3..3....0..0..0....0..1..2....0..3..0....0..0..0....2..1..1
		

Formula

Empirical recurrence of order 72 (see link above)

A231583 Number of n X 4 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

50, 602, 32650, 1245468, 38768838, 1453028265, 57099276134, 2144257250786, 79701582158514, 3015862229160377, 114494956350056953, 4326283671422314077, 163427418245733870700, 6184201660416852021556, 234047826007984885375504
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2013

Keywords

Comments

Column 4 of A231586.

Examples

			Some solutions for n=3
..1..0..1..1....2..0..0..0....1..0..0..0....1..1..2..2....0..0..0..2
..0..0..0..3....0..2..0..0....0..0..0..2....1..1..1..1....3..0..0..0
..0..0..0..0....0..0..0..1....1..0..1..3....3..3..1..1....2..1..0..3
		

Crossrefs

Cf. A231586.

A231584 Number of nX5 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

144, 2776, 381076, 38768838, 2912579313, 260228939106, 24813120747919, 2275463989704521, 205616812796559119, 18796952266641265062, 1725445840621150550236, 157941351701793475474726
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2013

Keywords

Comments

Column 5 of A231586

Examples

			Some solutions for n=2
..0..0..0..0..0....0..0..0..0..2....0..0..1..1..1....3..0..0..0..2
..2..0..0..2..0....0..3..0..0..3....0..0..3..1..1....0..0..0..0..2
		

A231585 Number of nX6 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

422, 12922, 5618444, 1453028265, 260228939106, 63676872069694, 16297132727558385, 3833026928529265733, 899070341715148291141, 216695260231841309307295, 52101389603112220215510578
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2013

Keywords

Comments

Column 6 of A231586

Examples

			Some solutions for n=2
..1..0..0..0..0..3....2..0..0..0..0..0....0..0..2..1..1..2....3..0..0..3..1..1
..0..0..1..0..0..3....0..0..1..2..0..0....0..0..1..1..1..2....2..0..0..1..1..1
		
Showing 1-5 of 5 results.