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.

A250856 Number of (4+1) X (n+1) 0..3 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

12311, 63631, 223933, 626416, 1499679, 3204951, 6279401, 11485528, 19866631, 32808359, 52106341, 80039896, 119451823, 173834271, 247420689, 345283856, 473439991, 638958943, 850080461, 1116336544, 1448679871, 1859618311
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Row 4 of A250853.

Formula

Empirical: a(n) = (76/9)*n^6 + (1595/12)*n^5 + (28765/36)*n^4 + (31373/12)*n^3 + (155683/36)*n^2 + (10223/3)*n + 1024.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(12311 - 22546*x + 37047*x^2 - 35749*x^3 + 21160*x^4 - 7167*x^5 + 1024*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A250857 Number of (5+1) X (n+1) 0..3 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

54410, 291165, 1043885, 2955136, 7134786, 15344785, 30214465, 55486360, 96292546, 159461501, 253855485, 390738440, 584174410, 851456481, 1213566241, 1695663760, 2327608090, 3144508285, 4187304941, 5503382256, 7147210610
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Row 5 of A250853.

Formula

Empirical: a(n) = (763/18)*n^6 + (1949/3)*n^5 + (136493/36)*n^4 + (72691/6)*n^3 + (693923/36)*n^2 + (43319/3)*n + 4096.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(54410 - 89705*x + 148340*x^2 - 141944*x^3 + 83994*x^4 - 28671*x^5 + 4096*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A250858 Number of (6+1) X (n+1) 0..3 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

233683, 1280447, 4648157, 13263136, 32201019, 69543783, 137379337, 252943672, 439905571, 729793879, 1163567333, 1793326952, 2684170987, 3916192431, 5586619089, 7812096208, 10731111667, 14506563727, 19328471341, 25416827024
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Row 6 of A250853.

Formula

Empirical: a(n) = 198*n^6 + (35807/12)*n^5 + (204911/12)*n^4 + (214827/4)*n^3 + (998209/12)*n^2 + (180451/3)*n + 16384.
Conjectures from Colin Barker, Nov 22 2018: (Start)
G.f.: x*(233683 - 355334*x + 592371*x^2 - 563481*x^3 + 333624*x^4 - 114687*x^5 + 16384*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A250859 Number of (7+1) X (n+1) 0..3 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

983950, 5480917, 20067117, 57570016, 140301126, 303858745, 601566177, 1109545432, 1932426406, 3209691541, 5122655965, 7902083112, 11836435822, 17280762921, 24666221281, 34510233360, 47427280222, 64140330037, 85492902061
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Row 7 of A250853.

Formula

Empirical: a(n) = (15887/18)*n^6 + (39464/3)*n^5 + (2674189/36)*n^4 + (462227/2)*n^3 + (12645859/36)*n^2 + (743119/3)*n + 65536.
Conjectures from Colin Barker, Nov 22 2018: (Start)
G.f.: x*(983950 - 1406733*x + 2363648*x^2 - 2238796*x^3 + 1326626*x^4 - 458751*x^5 + 65536*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.