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 1-5 of 5 results.

A208003 Number of n X 4 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

9, 81, 221, 536, 1711, 4993, 16742, 53411, 182247, 608142, 2095301, 7157363, 24822376, 85845073, 299033933, 1040987192, 3636447903, 12703622001, 44454269798, 155590727603, 545028524023, 1909557999406, 6693157243061
Offset: 1

Views

Author

R. H. Hardin, Feb 22 2012

Keywords

Comments

Column 4 of A208007.

Examples

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

Crossrefs

Cf. A208007.

Formula

Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 36*a(n-3) + 54*a(n-4) + 24*a(n-5) - 69*a(n-6) + 12*a(n-7) + 19*a(n-8) - 6*a(n-9) for n>10.
G.f.: x*(9 + 27*x - 238*x^2 - 223*x^3 + 1588*x^4 - 299*x^5 - 2044*x^6 + 767*x^7 + 603*x^8 - 234*x^9) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)*(1 - 2*x - 7*x^2 + 6*x^3)). - Colin Barker, Jun 26 2018

A208004 Number of nX5 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

14, 196, 618, 1711, 7016, 24512, 106503, 411848, 1787438, 7238503, 31139116, 128898716, 550671103, 2303973916, 9799872866, 41220045503, 174880633792, 737543803528, 3124620453847, 13195708252672, 55859776281926
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Column 5 of A208007

Examples

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

Formula

Empirical: a(n) = 9*a(n-1) -10*a(n-2) -106*a(n-3) +272*a(n-4) +170*a(n-5) -936*a(n-6) +306*a(n-7) +898*a(n-8) -558*a(n-9) -224*a(n-10) +190*a(n-11) +a(n-12) -11*a(n-13) for n>14

A208005 Number of nX6 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

22, 484, 1690, 4993, 24512, 90232, 486443, 2001968, 10846870, 47911153, 256232284, 1188682252, 6276190547, 30137070988, 157660283714, 775400765057, 4032502502920, 20159263106416, 104466312892411, 528009028013752
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Column 6 of A208007

Examples

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

Formula

Empirical: a(n) = 9*a(n-1) -2*a(n-2) -170*a(n-3) +392*a(n-4) +322*a(n-5) -1512*a(n-6) +474*a(n-7) +1498*a(n-8) -942*a(n-9) -376*a(n-10) +326*a(n-11) +a(n-12) -19*a(n-13) for n>14

A208006 Number of nX7 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

35, 1225, 4861, 16742, 106503, 486443, 3569728, 18874239, 139219755, 803098636, 5786553545, 35249727777, 248244598082, 1565658732841, 10842687856821, 69941258792526, 479065006181663, 3136670786824267, 21341996465201648
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Column 7 of A208007

Examples

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

Formula

Empirical: a(n) = 13*a(n-1) -6*a(n-2) -485*a(n-3) +1437*a(n-4) +3392*a(n-5) -14770*a(n-6) -2894*a(n-7) +44308*a(n-8) -15290*a(n-9) -46782*a(n-10) +23648*a(n-11) +18387*a(n-12) -9503*a(n-13) -2702*a(n-14) +1151*a(n-15) +129*a(n-16) -32*a(n-17) for n>18

A208002 Number of n X n 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 16, 92, 536, 7016, 90232, 3569728, 101519408, 13171648732, 783070626724, 349693561626416, 41247666769702640, 65777806787688875844, 14782056897493046845072, 86537979599825962734398012
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Diagonal of A208007

Examples

			Some solutions for n=4
..1..0..1..0....1..1..1..0....1..1..1..1....0..0..0..0....1..0..1..0
..1..0..1..1....1..0..1..1....0..1..1..1....0..1..1..0....1..1..1..0
..1..0..1..0....1..1..1..0....0..1..1..1....0..0..0..0....1..0..1..1
..1..0..1..0....1..0..1..1....0..1..1..1....0..1..1..0....1..1..1..0
		
Showing 1-5 of 5 results.