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.

A251093 Number of (n+1)X(n+1) 0..1 arrays with no 2X2 subblock having its minimum diagonal element less than its minimum antidiagonal element.

Original entry on oeis.org

13, 212, 9597, 1175519, 391088995, 353489877714, 867470863709067, 5781820357157777986, 104649732973693543280042, 5143991426222399264506760205, 686661619658213553959701988139993
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Diagonal of A251100

Examples

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

A251094 Number of (n+1) X (2+1) 0..1 arrays with no 2 X 2 subblock having its minimum diagonal element less than its minimum antidiagonal element.

Original entry on oeis.org

41, 212, 1109, 5817, 30517, 160086, 839758, 4405079, 23107524, 121214121, 635847599, 3335437865, 17496560104, 91780937840, 481451239589, 2525527648328, 13248049600905, 69494712657097, 364545365754237, 1912279634115658
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Examples

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

Crossrefs

Column 2 of A251100.

Formula

Empirical: a(n) = 7*a(n-1) - 11*a(n-2) + 10*a(n-3) - 3*a(n-4).
Empirical g.f.: x*(41 - 75*x + 76*x^2 - 24*x^3) / (1 - 7*x + 11*x^2 - 10*x^3 + 3*x^4). - Colin Barker, Nov 25 2018

A251095 Number of (n+1)X(3+1) 0..1 arrays with no 2X2 subblock having its minimum diagonal element less than its minimum antidiagonal element.

Original entry on oeis.org

129, 1109, 9597, 82814, 713769, 6151051, 53009570, 456842112, 3937123328, 33930621210, 292418287803, 2520096887534, 21718506027532, 187172766061609, 1613078004734497, 13901705381759445, 119806613163586853
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 3 of A251100

Examples

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

Formula

Empirical: a(n) = 16*a(n-1) -90*a(n-2) +285*a(n-3) -577*a(n-4) +763*a(n-5) -652*a(n-6) +352*a(n-7) -112*a(n-8) +16*a(n-9)

A251096 Number of (n+1)X(4+1) 0..1 arrays with no 2X2 subblock having its minimum diagonal element less than its minimum antidiagonal element.

Original entry on oeis.org

406, 5817, 82814, 1175519, 16697127, 237288487, 3372537762, 47933018061, 681254534234, 9682407527191, 137612328359012, 1955831221215641, 27797479224555547, 395074912980985813, 5615048233207846538
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 4 of A251100

Examples

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

Formula

Empirical: a(n) = 32*a(n-1) -408*a(n-2) +3073*a(n-3) -15730*a(n-4) +58157*a(n-5) -160070*a(n-6) +333703*a(n-7) -532992*a(n-8) +656691*a(n-9) -625063*a(n-10) +457960*a(n-11) -256393*a(n-12) +108609*a(n-13) -34260*a(n-14) +7752*a(n-15) -1136*a(n-16) +80*a(n-17)

A251097 Number of (n+1)X(5+1) 0..1 arrays with no 2X2 subblock having its minimum diagonal element less than its minimum antidiagonal element.

Original entry on oeis.org

1278, 30517, 713769, 16697127, 391088995, 9160138107, 214512524583, 5023196973684, 117627015646158, 2754453306431041, 64500662200661322, 1510403356276243957, 35368910899695159552, 828228987011430501703
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 5 of A251100

Examples

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

Formula

Empirical: a(n) = 64*a(n-1) -1764*a(n-2) +29700*a(n-3) -350488*a(n-4) +3107079*a(n-5) -21536824*a(n-6) +119757642*a(n-7) -543940823*a(n-8) +2045999565*a(n-9) -6444601609*a(n-10) +17157130467*a(n-11) -38908214534*a(n-12) +75659291228*a(n-13) -126869529554*a(n-14) +184336056227*a(n-15) -233006780681*a(n-16) +257060876816*a(n-17) -248098761256*a(n-18) +209731219435*a(n-19) -155260530399*a(n-20) +100445433948*a(n-21) -56541615273*a(n-22) +27492563839*a(n-23) -11423056137*a(n-24) +3995023081*a(n-25) -1152174020*a(n-26) +266437832*a(n-27) -47464016*a(n-28) +6119568*a(n-29) -509760*a(n-30) +20736*a(n-31)

A251098 Number of (n+1)X(6+1) 0..1 arrays with no 2X2 subblock having its minimum diagonal element less than its minimum antidiagonal element.

Original entry on oeis.org

4023, 160086, 6151051, 237288487, 9160138107, 353489877714, 13640572890821, 526395665662695, 20314343818684906, 783961045672945429, 30254198630466688429, 1167552996163615153868, 45057545754429137006661
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 6 of A251100

Examples

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

Formula

Empirical recurrence of order 57 (see link above)

A251099 Number of (n+1)X(7+1) 0..1 arrays with no 2X2 subblock having its minimum diagonal element less than its minimum antidiagonal element.

Original entry on oeis.org

12664, 839758, 53009570, 3372537762, 214512524583, 13640572890821, 867470863709067, 55168625738829232, 3508516188029302347, 223126143031289738192, 14189811432956928070475, 902408000057785985299460
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 7 of A251100

Examples

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