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.

Previous Showing 11-14 of 14 results.

A250816 Number of (4+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

1389, 4321, 10233, 20631, 37333, 62469, 98481, 148123, 214461, 300873, 411049, 548991, 719013, 925741, 1174113, 1469379, 1817101, 2223153, 2693721, 3235303, 3854709, 4559061, 5355793, 6252651, 7257693, 8379289, 9626121, 11007183
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 4 of A250812.

Formula

Empirical: a(n) = 13*n^4 + 121*n^3 + 439*n^2 + 573*n + 243.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(1389 - 2624*x + 2518*x^2 - 1214*x^3 + 243*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A250817 Number of (5+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

4356, 13735, 32745, 66291, 120304, 201741, 318585, 479845, 695556, 976779, 1335601, 1785135, 2339520, 3013921, 3824529, 4788561, 5924260, 7250895, 8788761, 10559179, 12584496, 14888085, 17494345, 20428701, 23717604, 27388531, 31469985
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 5 of A250812.

Formula

Empirical: a(n) = (171/4)*n^4 + 390*n^3 + (5627/4)*n^2 + (3575/2)*n + 729.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(4356 - 8045*x + 7630*x^2 - 3644*x^3 + 729*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A250818 Number of (6+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

13449, 42769, 102393, 207831, 377857, 634509, 1003089, 1512163, 2193561, 3082377, 4216969, 5638959, 7393233, 9527941, 12094497, 15147579, 18745129, 22948353, 27821721, 33432967, 39853089, 47156349, 55420273, 64725651, 75156537, 86800249
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 6 of A250812.

Formula

Empirical: a(n) = 136*n^4 + 1225*n^3 + 4402*n^2 + 5499*n + 2187.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(13449 - 24476*x + 23038*x^2 - 10934*x^3 + 2187*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A250819 Number of (7+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

41112, 131455, 315561, 641571, 1167796, 1962717, 3104985, 4683421, 6797016, 9554931, 13076497, 17491215, 22938756, 29568961, 37541841, 47027577, 58206520, 71269191, 86416281, 103858651, 123817332, 146523525, 172218601, 201154101
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 7 of A250812.

Formula

Empirical: a(n) = (1695/4)*n^4 + 3786*n^3 + (54287/4)*n^2 + (33539/2)*n + 6561.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(41112 - 74105*x + 69406*x^2 - 32804*x^3 + 6561*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
Previous Showing 11-14 of 14 results.

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