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 1-10 of 14 results. Next

A250845 Number of (n+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

100, 2457, 44797, 626416, 7134786, 69543783, 601566177, 4741091128, 34703305546, 239290928999, 1571038806045, 9901650019496, 60291096166330, 356456047451631, 2054525997174241, 11582011158980816, 64029681309724210, 347906811859565887
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Comments

Diagonal of A250853

Examples

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

Links

A250846 Number of (n+1) X (1+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

100, 543, 2670, 12311, 54410, 233683, 983950, 4085631, 16796370, 68555723, 278351030, 1125823351, 4540620730, 18274604163, 73435058910, 294750719471, 1182035443490, 4737241699003, 18976271027590, 75987005717991
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Comments

Column 1 of A250853.

Examples

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

Links

Formula

Empirical: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4); a(n) = (832*4^n-846*3^n+204*2^n+2)/12.
G.f.: x*(100 - 457*x + 740*x^2 - 384*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)) (conjectured). - Colin Barker, Jan 18 2018

A250847 Number of (n+1) X (2+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

400, 2457, 13097, 63631, 291165, 1280447, 5480917, 23024631, 95448605, 391939087, 1598379237, 6485763431, 26220548845, 105716192127, 425369781557, 1709000211031, 6858576189885, 27502054979567, 110211518943877
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Column 2 of A250853.

Formula

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (4838*4^n - 6300*3^n + 2214*2^n - 80)/12.
Empirical g.f.: x*(400 - 1543*x + 2527*x^2 - 1344*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 21 2018

A250848 Number of (n+1) X (3+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

1225, 8037, 44797, 223933, 1043885, 4648157, 20067117, 84805533, 353060845, 1454214877, 5943685037, 24157039133, 97778698605, 394573711197, 1588686176557, 6385947864733, 25637459261165, 102830957105117
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A250853.

Formula

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (18104*4^n - 26144*3^n + 10680*2^n - 644)/12.
Empirical g.f.: x*(1225 - 4213*x + 7302*x^2 - 3992*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). -Colin Barker, Nov 21 2018

A250849 Number of (n+1) X (4+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

3136, 21436, 123016, 626416, 2955136, 13263136, 57570016, 244213216, 1019415136, 4206874336, 17218194016, 70050978016, 283750743136, 1145667917536, 4614715410016, 18555090670816, 74509245399136, 298904020992736
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A250853.

Formula

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (52650*4^n - 80640*3^n + 35820*2^n - 2688)/12.
Empirical g.f.: 4*x*(784 - 2481*x + 4604*x^2 - 2571*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 21 2018

A250850 Number of (n+1) X (5+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

7056, 49599, 290646, 1499679, 7134786, 32201019, 140301126, 596722599, 2495502666, 10311967539, 42245985006, 171994777119, 697044608946, 2815440919659, 11343683099286, 45620754601239, 183221612905626
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A250853.

Formula

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (129528*4^n - 206190*3^n + 96660*2^n - 8190)/12.
Empirical g.f.: 9*x*(784 - 2329*x + 4624*x^2 - 2624*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 21 2018

A250851 Number of (n+1) X (6+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

14400, 103293, 614965, 3204951, 15344785, 69543783, 303858745, 1294875471, 5422612945, 22429374423, 91953454825, 374560079391, 1518555885505, 6135323831463, 24724903375705, 99451052025711, 399459752428465
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Column 6 of A250853.

Formula

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (282492*4^n - 462196*3^n + 224994*2^n - 20568)/12.
Empirical g.f.: x*(14400 - 40707*x + 86035*x^2 - 49444*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 21 2018

A250852 Number of (n+1) X (7+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

27225, 198297, 1195457, 6279401, 30214465, 137379337, 601566177, 2567402601, 10763029505, 44552408777, 182750596897, 744705474601, 3020091585345, 12204496276617, 49191016683617, 197884445031401, 794901482169985
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Column 7 of A250853.

Formula

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (562288*4^n - 939120*3^n + 470064*2^n - 45220)/12.
Empirical g.f.: x*(27225 - 73953*x + 165362*x^2 - 96024*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 21 2018

A250854 Number of (2+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

543, 2457, 8037, 21436, 49599, 103293, 198297, 356752, 608671, 993609, 1562493, 2379612, 3524767, 5095581, 7209969, 10008768, 13658527, 18354457, 24323541, 31827804, 41167743, 52685917, 66770697, 83860176, 104446239, 129078793
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Row 2 of A250853.

Formula

Empirical: a(n) = (2/9)*n^6 + (47/12)*n^5 + (953/36)*n^4 + (1141/12)*n^3 + (6527/36)*n^2 + 172*n + 64.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(543 - 1344*x + 2241*x^2 - 2231*x^3 + 1334*x^4 - 447*x^5 + 64*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)

A250855 Number of (3+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

2670, 13097, 44797, 123016, 290646, 614965, 1195457, 2172712, 3738406, 6146361, 9724685, 14888992, 22156702, 32162421, 45674401, 63612080, 87064702, 117311017, 155840061, 204373016, 264886150, 339634837, 431178657, 542407576, 676569206
Offset: 1

Views

Author

R. H. Hardin, Nov 28 2014

Keywords

Examples

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

Links

Crossrefs

Row 3 of A250853.

Formula

Empirical: a(n) = (3/2)*n^6 + (74/3)*n^5 + (621/4)*n^4 + (3161/6)*n^3 + (3691/4)*n^2 + 783*n + 256.
Conjectures from Colin Barker, Nov 21 2018: (Start)
G.f.: x*(2670 - 5593*x + 9188*x^2 - 8976*x^3 + 5326*x^4 - 1791*x^5 + 256*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)
Showing 1-10 of 14 results. Next

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