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.

A208374 Number of n X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 16, 72, 420, 2176, 10660, 60984, 340816, 1846240, 11076228, 66303360, 390426916, 2456007216, 15586002640, 98058552648, 645057461220, 4299810563584, 28563593727716, 195777751059000, 1361449965542992, 9468978890210480
Offset: 1

Views

Author

R. H. Hardin Feb 25 2012

Keywords

Comments

Diagonal of A208379

Examples

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

Links

A208375 Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

10, 100, 240, 420, 640, 900, 1200, 1540, 1920, 2340, 2800, 3300, 3840, 4420, 5040, 5700, 6400, 7140, 7920, 8740, 9600, 10500, 11440, 12420, 13440, 14500, 15600, 16740, 17920, 19140, 20400, 21700, 23040, 24420, 25840, 27300, 28800, 30340, 31920, 33540
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Column 4 of A208379.

Examples

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

Links

Crossrefs

Cf. A208379.

Formula

Empirical: a(n) = 20*n^2 + 40*n - 60 for n>1.
Conjectures from Colin Barker, Jul 02 2018: (Start)
G.f.: 10*x*(1 + 7*x - 3*x^2 - x^3) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
(End)

A208376 Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

16, 256, 704, 1344, 2176, 3200, 4416, 5824, 7424, 9216, 11200, 13376, 15744, 18304, 21056, 24000, 27136, 30464, 33984, 37696, 41600, 45696, 49984, 54464, 59136, 64000, 69056, 74304, 79744, 85376, 91200, 97216, 103424, 109824, 116416, 123200, 130176
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Column 5 of A208379.

Examples

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

Links

Crossrefs

Cf. A208379.

Formula

Empirical: a(n) = 96*n^2 - 32*n - 64 for n>1.
Conjectures from Colin Barker, Jul 02 2018: (Start)
G.f.: 16*x*(1 + 13*x - x^2 - x^3) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
(End)

A208377 Number of n X 6 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

26, 676, 2080, 4212, 7072, 10660, 14976, 20020, 25792, 32292, 39520, 47476, 56160, 65572, 75712, 86580, 98176, 110500, 123552, 137332, 151840, 167076, 183040, 199732, 217152, 235300, 254176, 273780, 294112, 315172, 336960, 359476, 382720
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Column 6 of A208379.

Examples

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

Links

Crossrefs

Cf. A208379.

Formula

Empirical: a(n) = 364*n^2 - 416*n + 52 for n>1.
Conjectures from Colin Barker, Jul 02 2018: (Start)
G.f.: 26*x*(1 + 23*x + 5*x^2 - x^3) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
(End)

A208378 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

42, 1764, 6216, 13860, 25200, 40740, 60984, 86436, 117600, 154980, 199080, 250404, 309456, 376740, 452760, 538020, 633024, 738276, 854280, 981540, 1120560, 1271844, 1435896, 1613220, 1804320, 2009700, 2229864, 2465316, 2716560, 2984100, 3268440
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Column 7 of A208379.

Examples

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

Links

Crossrefs

Cf. A208379.

Formula

Empirical: a(n) = 84*n^3 + 840*n^2 - 1344*n + 420 for n>1.
Conjectures from Colin Barker, Jul 02 2018: (Start)
G.f.: 42*x*(1 + 38*x - 14*x^2 - 14*x^3 + x^4) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
(End)

A208380 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

8, 64, 108, 420, 1344, 4212, 13860, 44880, 144540, 468852, 1517184, 4906980, 15883764, 51401040, 166325292, 538259268, 1741843392, 5636673684, 18240740100, 59028275280, 191019298428, 618151779156, 2000381177088, 6473368570500
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Row 4 of A208379.

Examples

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

Links

Crossrefs

Cf. A208379.

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) + 9*a(n-3) + 5*a(n-4) - 2*a(n-5) + 4*a(n-6) for n>8.
Empirical g.f.: 4*x*(2 + 14*x + 3*x^2 - 4*x^3 - 31*x^4 - 22*x^5 + 12*x^6 - 16*x^7) / ((1 - 2*x - 4*x^2)*(1 + x + 2*x^2 - x^3 + x^4)). - Colin Barker, Jul 02 2018

A208381 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

10, 100, 144, 640, 2176, 7072, 25200, 87040, 296560, 1028128, 3545856, 12198016, 42085264, 145092160, 499958928, 1723635712, 5941670272, 20479942816, 70597050480, 243353573632, 838843117552, 2891546321440, 9967326856704
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Row 5 of A208379.

Examples

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

Links

Crossrefs

Cf. A208379.

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) + 13*a(n-3) + 8*a(n-4) - 3*a(n-5) + 9*a(n-6) for n>8.
Empirical g.f.: 2*x*(5 + 45*x + 2*x^2 - 17*x^3 - 210*x^4 - 153*x^5 + 81*x^6 - 162*x^7) / (1 - x - 4*x^2 - 13*x^3 - 8*x^4 + 3*x^5 - 9*x^6). - Colin Barker, Jul 02 2018

A208382 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

12, 144, 180, 900, 3200, 10660, 40740, 148240, 526900, 1931300, 7015680, 25336420, 92086020, 334206800, 1211147700, 4394975940, 15944933760, 57827661860, 209781161700, 761003136400, 2760390765620, 10013327220580, 36323344673280
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Row 6 of A208379.

Examples

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

Links

Crossrefs

Cf. A208379.

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) + 17*a(n-3) + 11*a(n-4) - 4*a(n-5) + 16*a(n-6) for n>8.
Empirical g.f.: 4*x*(3 + 33*x - 3*x^2 - 15*x^3 - 250*x^4 - 184*x^5 + 96*x^6 - 256*x^7) / (1 - x - 4*x^2 - 17*x^3 - 11*x^4 + 4*x^5 - 16*x^6). - Colin Barker, Jul 02 2018

A208383 Number of 7 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

14, 196, 216, 1200, 4416, 14976, 60984, 231744, 851400, 3276624, 12438144, 46737936, 177585096, 673147200, 2544020136, 9639951936, 36515578944, 138204393264, 523395873000, 1982108510304, 7504603109784, 28417632893376
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Comments

Row 7 of A208379.

Examples

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

Links

Crossrefs

Cf. A208379.

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) + 21*a(n-3) + 14*a(n-4) - 5*a(n-5) + 25*a(n-6) for n>8.
Empirical g.f.: 2*x*(7 + 91*x - 18*x^2 - 47*x^3 - 980*x^4 - 725*x^5 + 375*x^6 - 1250*x^7) / (1 - x - 4*x^2 - 21*x^3 - 14*x^4 + 5*x^5 - 25*x^6). - Colin Barker, Jul 02 2018
Showing 1-9 of 9 results.

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

Content is available under The OEIS End-User License Agreement.