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.

A201447 Number of nX4 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

1, 9, 29, 112, 261, 846, 1720, 4193, 8065, 16693, 29073, 55954, 90874, 158301, 249828, 409302, 611841, 962288, 1392970, 2091478, 2957586, 4286258, 5893598, 8347259, 11221370, 15440747, 20464931, 27577548, 35834857, 47497364, 60856456, 79217039
Offset: 1

Views

Author

R. H. Hardin Dec 01 2011

Keywords

Comments

Column 4 of A201451

Examples

			Some solutions for n=10
..0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..1
..0..0..0..1....0..1..1..1....0..0..1..1....0..0..0..0....0..0..1..1
..0..1..1..1....0..1..1..1....0..0..1..1....0..0..2..2....0..1..2..3
..0..1..2..2....0..1..1..1....0..0..1..1....1..1..2..2....0..1..2..3
..0..2..2..2....0..1..2..3....0..1..1..1....1..1..2..3....0..1..2..3
..1..2..2..3....0..2..2..3....2..2..3..3....1..1..2..3....0..1..2..3
..1..2..2..3....0..2..2..3....2..2..3..3....1..1..2..3....0..1..2..3
..1..2..3..3....2..2..2..3....2..2..3..3....1..1..2..3....1..1..2..3
..1..3..3..3....2..3..3..3....2..2..3..3....2..3..3..3....2..2..2..3
..1..3..3..3....2..3..3..3....2..2..3..3....2..3..3..3....2..3..3..3

Links

A201445 Number of n X 2 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

6, 2, 21, 9, 56, 13, 110, 32, 198, 41, 315, 78, 480, 94, 684, 155, 950, 180, 1265, 271, 1656, 307, 2106, 434, 2646, 483, 3255, 652, 3968, 716, 4760, 933, 5670, 1014, 6669, 1285, 7800, 1385, 9030, 1716, 10406, 1837, 11891, 2234, 13536, 2378, 15300, 2847
Offset: 1

Views

Author

R. H. Hardin, Dec 01 2011

Keywords

Comments

Column 2 of A201451.

Examples

			Some solutions for n=10:
..0..0....0..0....0..1....0..1....0..2....0..0....0..0....0..0....0..1....0..0
..0..1....0..1....0..1....0..1....0..2....0..1....0..1....0..0....0..1....0..1
..0..2....0..1....0..2....0..2....0..2....0..1....0..2....0..1....0..1....0..2
..0..2....0..2....0..2....0..2....0..2....0..1....0..2....1..1....0..2....0..2
..1..2....1..2....0..2....0..2....0..2....1..1....1..2....1..1....0..2....1..2
..1..2....1..2....1..2....1..3....1..3....2..2....1..3....2..2....1..2....1..2
..1..2....1..2....1..2....1..3....1..3....2..3....1..3....2..3....1..3....1..3
..1..3....2..3....1..3....1..3....1..3....2..3....1..3....2..3....2..3....1..3
..3..3....3..3....3..3....2..3....1..3....2..3....2..3....2..3....2..3....2..3
..3..3....3..3....3..3....2..3....1..3....3..3....2..3....3..3....3..3....3..3

Links

Crossrefs

Cf. A201451.

Formula

Empirical: a(n) = a(n-2) +3*a(n-4) -3*a(n-6) -3*a(n-8) +3*a(n-10) +a(n-12) -a(n-14).
Subsequences for n modulo 4 = 1,2,3,0:
p=(n+3)/4: a(n) = 8*p^3 - 2*p^2
q=(n+2)/4: a(n) = (4/3)*q^3 + (1/2)*q^2 + (1/6)*q
r=(n+1)/4: a(n) = 8*r^3 + 10*r^2 + 3*r
s=(n+0)/4: a(n) = (4/3)*s^3 + (7/2)*s^2 + (19/6)*s + 1.
Empirical g.f.: x*(6 + 2*x + 15*x^2 + 7*x^3 + 17*x^4 - 2*x^5 + 9*x^6 - 2*x^7 + x^8 + 3*x^9 + x^11 - x^13) / ((1 - x)^4*(1 + x)^4*(1 + x^2)^3). - Colin Barker, May 23 2018

A201446 Number of nX3 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

4, 21, 52, 29, 246, 701, 844, 426, 2478, 5990, 6334, 2358, 13766, 29096, 26976, 9735, 50294, 100963, 89428, 29011, 149198, 283043, 237216, 75948, 368044, 680922, 557638, 169158, 816740, 1464838, 1163616, 350485, 1633894, 2887309, 2261850
Offset: 1

Views

Author

R. H. Hardin Dec 01 2011

Keywords

Comments

Column 3 of A201451

Examples

			Some solutions for n=10
..0..0..2....0..0..0....0..0..0....0..0..2....0..0..0....0..0..0....0..0..1
..0..0..2....0..0..1....0..0..0....0..1..2....0..0..1....0..1..2....0..1..1
..0..1..2....0..0..2....0..0..1....0..1..2....0..1..2....0..1..2....0..1..2
..0..1..3....1..1..3....1..1..2....0..1..2....0..2..3....0..1..2....0..2..2
..0..1..3....1..1..3....1..1..2....0..1..2....1..2..3....0..1..2....0..2..2
..0..1..3....1..1..3....1..2..2....0..1..2....1..2..3....1..1..2....0..2..3
..1..2..3....1..2..3....1..2..2....1..1..3....1..2..3....1..3..3....0..2..3
..1..2..3....2..2..3....2..3..3....1..2..3....1..2..3....2..3..3....1..2..3
..1..2..3....2..2..3....3..3..3....3..3..3....1..2..3....2..3..3....1..3..3
..2..2..3....2..2..3....3..3..3....3..3..3....1..3..3....2..3..3....1..3..3

Links

Formula

Empirical: a(n) = 2*a(n-4) +3*a(n-8) -8*a(n-12) -a(n-16) +10*a(n-20) -5*a(n-24) +5*a(n-32) -10*a(n-36) +a(n-40) +8*a(n-44) -3*a(n-48) -2*a(n-52) +a(n-56)

A201448 Number of nX5 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

4, 56, 246, 261, 4544, 22324, 45532, 32314, 313710, 1126721, 1675002, 879801, 7177332, 20808117, 25958138, 11930250, 83429402, 215418299, 242046848, 99077372, 640294388, 1516885224, 1571234990, 603846146, 3627055278
Offset: 1

Views

Author

R. H. Hardin Dec 01 2011

Keywords

Comments

Column 5 of A201451

Examples

			Some solutions for n=8
..0..0..0..1..2....0..0..0..1..2....0..0..0..0..1....0..0..0..0..2
..0..1..1..1..2....0..0..1..1..2....0..0..1..1..2....0..0..0..2..2
..0..1..1..1..3....0..0..1..1..2....0..1..1..1..2....0..1..1..2..3
..0..1..2..2..3....0..0..1..1..2....0..1..1..1..2....0..1..1..2..3
..0..1..2..2..3....0..1..1..1..2....0..1..2..2..2....0..1..1..3..3
..0..1..2..3..3....2..2..2..3..3....0..2..2..3..3....1..1..2..3..3
..0..2..2..3..3....2..3..3..3..3....2..3..3..3..3....1..1..2..3..3
..0..2..3..3..3....2..3..3..3..3....2..3..3..3..3....2..2..2..3..3

Links

A201449 Number of nX6 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

6, 13, 701, 846, 22324, 16334, 363693, 211755, 3708666, 1743841, 27486101, 11523462, 159251638, 59366033, 763865999, 265448264, 3148137956, 1014298362, 11451837500, 3516665645, 37535616517, 10943450873, 112627454165, 31695873391
Offset: 1

Views

Author

R. H. Hardin Dec 01 2011

Keywords

Comments

Column 6 of A201451

Examples

			Some solutions for n=6
..0..0..0..0..1..2....0..0..0..1..1..1....0..0..0..1..1..1....0..0..0..1..1..1
..0..0..0..0..1..2....0..0..1..1..1..2....0..0..0..1..1..1....0..0..1..2..2..2
..0..1..1..1..2..3....0..0..1..2..2..3....0..0..0..1..2..2....0..0..1..2..2..3
..1..1..2..2..3..3....0..1..2..2..2..3....1..2..2..2..2..3....0..0..1..2..2..3
..1..1..2..2..3..3....0..2..2..3..3..3....1..2..2..3..3..3....1..1..1..2..3..3
..2..2..3..3..3..3....1..2..3..3..3..3....2..3..3..3..3..3....2..3..3..3..3..3

Links

A201450 Number of n X 7 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

4, 110, 844, 1720, 45532, 363693, 1129682, 1136762, 16354832, 80822317, 164740812, 118019739, 1269643884, 4872612379, 7910355612, 4617454222, 41308142036, 133824389250, 186755344178, 94854691897, 750329582592, 2169912953058
Offset: 1

Views

Author

R. H. Hardin, Dec 01 2011

Keywords

Examples

			Some solutions for n=5:
..0..0..0..0..1..1..1....0..0..0..1..1..1..2....0..0..0..0..0..1..2
..0..0..1..1..1..1..3....0..0..1..1..1..1..3....0..0..1..1..1..2..2
..0..0..1..1..2..2..3....0..1..1..2..2..2..3....0..1..1..1..2..2..3
..0..2..2..2..3..3..3....0..2..2..2..2..2..3....0..1..1..2..2..2..3
..2..2..2..2..3..3..3....0..3..3..3..3..3..3....3..3..3..3..3..3..3

Links

Crossrefs

Column 7 of A201451.

A201444 Number of n X n 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

Original entry on oeis.org

4, 2, 52, 112, 4544, 16334, 1129682, 5464208, 458459214, 2605975384, 253569083138, 1617730690396
Offset: 1

Views

Author

R. H. Hardin Dec 01 2011

Keywords

Comments

Diagonal of A201451

Examples

			Some solutions for n=6
..0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..1..2..2....0..0..0..0..1..1
..0..0..1..2..2..2....0..0..0..0..1..1....0..0..1..1..2..3....0..0..0..0..2..2
..0..0..1..2..3..3....0..1..1..1..1..1....0..1..1..2..2..3....0..1..1..1..2..2
..1..1..2..2..3..3....2..2..2..2..2..3....0..1..1..2..2..3....1..1..2..2..2..2
..1..1..2..2..3..3....2..2..2..3..3..3....0..1..1..2..2..3....1..1..2..3..3..3
..1..1..2..3..3..3....2..3..3..3..3..3....0..3..3..3..3..3....3..3..3..3..3..3
Showing 1-7 of 7 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.