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 1-6 of 6 results.

A252980 Number of n X 5 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

6, 41, 266, 1247, 4657, 67537, 433401, 1481460, 3510600, 6637020, 10878576, 16235268, 22707096, 30294060, 38996160, 48813396, 59745768, 71793276, 84955920, 99233700, 114626616, 131134668, 148757856, 167496180, 187349640, 208318236
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Column 5 of A252983.

Examples

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

Links

Crossrefs

Cf. A252983.

Formula

Empirical: a(n) = 557568*n^2 - 7467372*n + 25553940 for n>8.
Conjectures from Colin Barker, Mar 20 2018: (Start)
G.f.: x*(6 + 23*x + 161*x^2 + 566*x^3 + 1673*x^4 + 57041*x^5 + 243514*x^6 + 379211*x^7 + 298886*x^8 + 116199*x^9 + 17856*x^10) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
(End)

A252981 Number of nX6 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

10, 85, 851, 8487, 67537, 432842, 5672484, 36112108, 129234988, 322183180, 635379492, 1074743076, 1640984356, 2334103332, 3154100004, 4100974372, 5174726436, 6375356196, 7702863652, 9157248804, 10738511652, 12446652196
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Column 6 of A252983

Examples

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

Links

Formula

Empirical: a(n) = 63438848*n^2 - 1019729920*n + 4176308004 for n>10

A252982 Number of nX7 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

15, 145, 1836, 27905, 433401, 5672484, 60650883, 766674140, 4970634131, 18692194423, 49050683133, 101029007619, 176694157069, 276519316503, 400550856993, 548788778539, 721233081141, 917883764799, 1138740829513
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Column 7 of A252983

Examples

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

Links

Formula

Empirical: a(n) = 12103190528*n^2 - 226960984822*n + 1081747760523 for n>12

A252977 Number of n X n nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

0, 0, 1, 68, 4657, 432842, 60650883, 13458882036, 4857082197177, 2895119784219358, 2877300288177184239, 4796057029604523514392, 13457301734652492685623300, 63707500883584152928303777296
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Diagonal of A252983

Examples

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

Links

A252978 Number of n X 3 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

1, 1, 1, 33, 266, 851, 1836, 3221, 5006, 7191, 9776, 12761, 16146, 19931, 24116, 28701, 33686, 39071, 44856, 51041, 57626, 64611, 71996, 79781, 87966, 96551, 105536, 114921, 124706, 134891, 145476, 156461, 167846, 179631, 191816, 204401, 217386
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A252983.

Formula

Empirical: a(n) = 200*n^2 - 1615*n + 3341 for n>4.
Conjectures from Colin Barker, Dec 07 2018: (Start)
G.f.: x*(1 - 2*x + x^2 + 32*x^3 + 169*x^4 + 151*x^5 + 48*x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)

A252979 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

3, 13, 33, 68, 1247, 8487, 27905, 62977, 114433, 182273, 266497, 367105, 484097, 617473, 767233, 933377, 1115905, 1314817, 1530113, 1761793, 2009857, 2274305, 2555137, 2852353, 3165953, 3495937, 3842305, 4205057, 4584193, 4979713, 5391617
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A252983.

Formula

Empirical: a(n) = 8192*n^2 - 87808*n + 241153 for n>6.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x*(3 + 4*x + 3*x^2 + 5*x^3 + 1129*x^4 + 4917*x^5 + 6117*x^6 + 3476*x^7 + 730*x^8) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
(End)
Showing 1-6 of 6 results.

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