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.

A229795 Number of 2 X 2 0..n arrays with rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

7, 29, 86, 205, 421, 777, 1324, 2121, 3235, 4741, 6722, 9269, 12481, 16465, 21336, 27217, 34239, 42541, 52270, 63581, 76637, 91609, 108676, 128025, 149851, 174357, 201754, 232261, 266105, 303521, 344752, 390049, 439671, 493885, 552966, 617197
Offset: 1

Views

Author

R. H. Hardin, Sep 29 2013

Keywords

Examples

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

Links

Crossrefs

Row 2 of A229794.

Formula

Empirical: a(n) = (1/3)*n^4 + (7/6)*n^3 + (13/6)*n^2 + (7/3)*n + 1.
Conjectures from Colin Barker, Sep 21 2018: (Start)
G.f.: x*(7 - 6*x + 11*x^2 - 5*x^3 + 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)

A229796 Number of 3 X 3 0..n arrays with rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

45, 1169, 14178, 102251, 520017, 2066505, 6842284, 19692165, 50724037, 119421753, 261015470, 535936479, 1043365337, 1940082033, 3466044984, 5978361865, 9995569629, 16254413569, 25781605914, 39983353235, 60755768865, 90619631609
Offset: 1

Views

Author

R. H. Hardin, Sep 29 2013

Keywords

Examples

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

Links

Crossrefs

Row 3 of A229794.

Formula

Empirical: a(n) = (1/20)*n^9 + (11/24)*n^8 + (329/180)*n^7 + (1601/360)*n^6 + (545/72)*n^5 + (347/36)*n^4 + (3367/360)*n^3 + (313/45)*n^2 + (37/10)*n + 1.
Conjectures from Colin Barker, Sep 21 2018: (Start)
G.f.: x*(45 + 719*x + 4513*x^2 + 7676*x^3 + 4687*x^4 + 420*x^5 + 121*x^6 - 46*x^7 + 10*x^8 - x^9) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)

A229797 Number of 4X4 0..n arrays with rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

650, 250841, 21907055, 733861607, 13111482259, 150943642765, 1257194266246, 8170451731089, 43642376268844, 198859490805437, 794550500198885, 2842727725991231, 9257049674121653, 27794351169785161, 77754305616698860
Offset: 1

Views

Author

R. H. Hardin, Sep 29 2013

Keywords

Comments

Row 4 of A229794

Examples

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

Links

Formula

Empirical: a(n) = (1/252)*n^16 + (17/252)*n^15 + (1349/2520)*n^14 + (26531/10080)*n^13 + (2597/288)*n^12 + (691/30)*n^11 + (694109/15120)*n^10 + (2229581/30240)*n^9 + (5469/56)*n^8 + (546263/5040)*n^7 + (73249/720)*n^6 + (7297/90)*n^5 + (47305/864)*n^4 + (16739/540)*n^3 + (36263/2520)*n^2 + (533/105)*n + 1

A229798 Number of 5X5 0..n arrays with rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

24520, 318174607, 348053502590, 83399309397669, 7470491620551006, 337176110123479647, 9191448163080152260, 170263099219981493623, 2323791090717304237514, 24760438397023153230241, 214990023150964441381574
Offset: 1

Views

Author

R. H. Hardin, Sep 29 2013

Keywords

Comments

Row 5 of A229794

Examples

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

Links

A229799 Number of 6X6 0..n arrays with rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

2625117, 2533164987353, 60704077222861152, 161327438675038562165, 103937249022030445057526, 24982715242286897029686383, 2907883712766278818772179090, 194172351727597419593410162517
Offset: 1

Views

Author

R. H. Hardin, Sep 29 2013

Keywords

Comments

Row 6 of A229794

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..1..1....0..0..0..0..1..1....0..0..0..0..0..1....0..0..0..0..1..1
..0..0..1..1..0..1....0..0..1..1..0..0....0..0..0..1..1..0....0..0..0..1..0..1
..0..1..0..1..1..0....0..1..1..1..0..0....0..0..1..1..1..0....0..0..1..0..0..0
..0..1..1..1..1..1....1..0..0..0..0..1....0..1..0..0..1..0....0..0..1..1..0..1
..1..0..0..1..1..1....1..0..0..0..0..1....0..1..1..1..0..0....0..0..1..1..1..1

Links

A229800 Number of 7X7 0..n arrays with rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

836488618, 132171590850720635, 122233352821430587249163, 5614157616366023545393324521, 37429493951522536724740382711237, 65195331584280599878464161050608017
Offset: 1

Views

Author

R. H. Hardin, Sep 29 2013

Keywords

Comments

Row 7 of A229794

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....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..1....0..0..0..0..0..0..1
..0..0..0..0..0..1..1....0..0..0..0..1..1..0....0..0..0..0..0..0..1
..0..0..1..1..1..0..0....0..0..0..0..1..1..0....0..0..0..1..1..1..1
..0..1..0..0..1..1..1....0..0..0..1..0..1..0....0..1..1..0..1..1..1
..1..0..0..0..1..0..0....1..1..1..0..1..1..1....1..0..0..0..0..0..1
Showing 1-6 of 6 results.

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