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 1-9 of 9 results.

A208008 Number of n X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

2, 16, 90, 841, 5952, 43264, 393049, 4084441, 32673396, 334012176, 3665311664, 37536737536, 385814058880, 4801282939489, 53629177761313, 628423124320161, 7905277739708518, 101862335149216849, 1250237739999352500
Offset: 1

Views

Author

R. H. Hardin, Feb 22 2012

Keywords

Comments

Diagonal of A208013.

Examples

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

Links

Crossrefs

Cf. A208013.

A208009 Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

9, 81, 261, 841, 1943, 4489, 8643, 16641, 28509, 48841, 77129, 121801, 181131, 269361, 382503, 543169, 743633, 1018081, 1353069, 1798281, 2331999, 3024121, 3841451, 4879681, 6090213, 7601049, 9343473, 11485321, 13932179, 16900321
Offset: 1

Views

Author

R. H. Hardin, Feb 22 2012

Keywords

Comments

Column 4 of A208013.

Examples

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

Links

Crossrefs

Cf. A208013.

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) - 5*a(n-4) + 20*a(n-5) - 20*a(n-7) + 5*a(n-8) + 10*a(n-9) - 4*a(n-10) - 2*a(n-11) + a(n-12).
Empirical g.f.: x*(9 + 63*x + 63*x^2 + 85*x^3 + 72*x^4 + 74*x^5 - 12*x^6 - 6*x^7 + 15*x^8 - x^9 - 3*x^10 + x^11) / ((1 - x)^7*(1 + x)^5). - Colin Barker, Jun 26 2018

A208010 Number of nX5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

13, 169, 624, 2304, 5952, 15376, 32860, 70225, 132765, 251001, 434868, 753424, 1222144, 1982464, 3053952, 4704561, 6951645, 10272025, 14666080, 20939776, 29048448, 40297104, 54548364, 73839649, 97865677, 129709321, 168784980
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Column 5 of A208013

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) +6*a(n-2) -14*a(n-3) -14*a(n-4) +42*a(n-5) +14*a(n-6) -70*a(n-7) +70*a(n-9) -14*a(n-10) -42*a(n-11) +14*a(n-12) +14*a(n-13) -6*a(n-14) -2*a(n-15) +a(n-16)

A208011 Number of nX6 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

19, 361, 1482, 6084, 16224, 43264, 92560, 198025, 369795, 690561, 1175034, 1999396, 3178672, 5053504, 7627464, 11512449, 16676595, 24157225, 33844690, 47416996, 64618224, 88059456, 117234312, 156075049, 203673379, 265787809, 340895730
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Column 6 of A208013

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) +6*a(n-2) -14*a(n-3) -14*a(n-4) +42*a(n-5) +14*a(n-6) -70*a(n-7) +70*a(n-9) -14*a(n-10) -42*a(n-11) +14*a(n-12) +14*a(n-13) -6*a(n-14) -2*a(n-15) +a(n-16)

A208012 Number of nX7 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

28, 784, 3808, 18496, 55624, 167281, 393049, 923521, 1860496, 3748096, 6791488, 12306064, 20630548, 34586161, 54628609, 86285521, 130008844, 195888016, 284062816, 411927616, 578699848, 812991169, 1112035513, 1521078001
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Column 7 of A208013

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) +6*a(n-2) -14*a(n-3) -14*a(n-4) +42*a(n-5) +14*a(n-6) -70*a(n-7) +70*a(n-9) -14*a(n-10) -42*a(n-11) +14*a(n-12) +14*a(n-13) -6*a(n-14) -2*a(n-15) +a(n-16)

A208014 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

9, 81, 225, 841, 2304, 6084, 18496, 53824, 150544, 435600, 1263376, 3610000, 10368400, 29899024, 85895824, 246741264, 709902736, 2041232400, 5866947216, 16869853456, 48507419536, 139454446096, 400947305616, 1152814510864
Offset: 1

Views

Author

R. H. Hardin, Feb 22 2012

Keywords

Comments

Row 4 of A208013.

Examples

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

Links

Crossrefs

Cf. A208013.

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 10*a(n-3) + 4*a(n-4) - 8*a(n-5) - 16*a(n-6) for n>8.
Empirical g.f.: x*(9 + 72*x + 126*x^2 + 364*x^3 + 167*x^4 - 404*x^5 - 714*x^6 - 148*x^7) / ((1 + 2*x^2 - 4*x^3)*(1 - x - 4*x^2 - 4*x^3)). - Colin Barker, Jun 26 2018

A208015 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

12, 144, 420, 1943, 5952, 16224, 55624, 181192, 545140, 1737120, 5591900, 17461000, 55016920, 175036148, 552196708, 1741059012, 5511897568, 17422085700, 55006038672, 173881945232, 549639384692, 1736473292204, 5487493400532
Offset: 1

Views

Author

R. H. Hardin, Feb 22 2012

Keywords

Comments

Row 5 of A208013.

Examples

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

Links

Crossrefs

Cf. A208013.

Formula

Empirical: a(n) = a(n-1) + 23*a(n-3) + 6*a(n-4) + 6*a(n-5) - 108*a(n-6) - 72*a(n-7) + 216*a(n-9) for n>11.
Empirical g.f.: x*(12 + 132*x + 276*x^2 + 1247*x^3 + 625*x^4 - 324*x^5 - 7377*x^6 - 9090*x^7 - 846*x^8 + 17064*x^9 + 7884*x^10) / (1 - x - 23*x^3 - 6*x^4 - 6*x^5 + 108*x^6 + 72*x^7 - 216*x^9). - Colin Barker, Jun 26 2018

A208016 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

16, 256, 784, 4489, 15376, 43264, 167281, 609961, 1974025, 6927424, 24750625, 84456100, 291931396, 1024704121, 3549895561, 12285283921, 42796024384, 148698928225, 515713569424, 1792246207504, 6227984421649, 21622397700121
Offset: 1

Views

Author

R. H. Hardin, Feb 22 2012

Keywords

Comments

Row 6 of A208013.

Examples

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

Links

Crossrefs

Cf. A208013.

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) + 21*a(n-3) + 9*a(n-4) - 27*a(n-5) - 81*a(n-6) for n>8.
Empirical g.f.: x*(16 + 240*x + 480*x^2 + 2601*x^3 + 3015*x^4 - 3915*x^5 - 15228*x^6 - 8505*x^7) / ((1 + 3*x^2 - 9*x^3)*(1 - x - 6*x^2 - 9*x^3)). - Colin Barker, Jun 26 2018

A208017 Number of 7Xn 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

20, 400, 1260, 8643, 32860, 92560, 393049, 1578401, 5340405, 20121640, 78251775, 284274270, 1051011118, 3983096719, 14785680541, 54778074707, 205202336088, 765281117395, 2844826058100, 10615121655468, 39598654722769
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Row 7 of A208013

Examples

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

Links

Formula

Empirical: a(n) = a(n-1) +43*a(n-3) +12*a(n-4) +12*a(n-5) -432*a(n-6) -288*a(n-7) +1728*a(n-9) for n>11
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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