A301999 -id:A301999 - cp's OEIS frontend

A301994 Number of n X 3 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 5, 15, 48, 155, 499, 1602, 5137, 16467, 52784, 169199, 542375, 1738618, 5573261, 17865479, 57269040, 183579891, 588478091, 1886407378, 6047009817, 19384109803, 62137109808, 199184819687, 638500768991, 2046758546378, 6561026627701

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Column 3 of A301999.

			Some solutions for n=5:
  0 0 0   0 0 1   0 0 1   0 0 1   0 0 1   0 0 0   0 0 1
  1 1 0   1 1 0   1 1 1   0 1 1   1 1 1   1 1 0   1 1 1
  1 0 0   0 0 0   1 0 0   0 0 1   1 1 1   0 0 0   1 0 0
  1 1 0   0 1 1   1 1 0   0 1 0   1 0 0   0 1 0   1 1 1
  1 0 0   1 0 0   1 0 0   1 0 0   0 1 1   1 0 0   0 0 0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A301999, A049219.

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) + 4*a(n-3).

Empirical: partial sums of A049219. - Sean A. Irvine, Jul 13 2022

A301995 Number of nX4 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

2, 8, 26, 74, 200, 530, 1394, 3656, 9578, 25082, 65672, 171938, 450146, 1178504, 3085370, 8077610, 21147464, 55364786, 144946898, 379475912, 993480842, 2600966618, 6809419016, 17827290434, 46672452290, 122190066440, 319897747034

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Column 4 of A301999.

			Some solutions for n=5
..0..0..1..1. .0..0..1..0. .0..0..1..1. .0..0..1..1. .0..0..1..1
..0..0..0..0. .0..1..0..0. .1..1..0..0. .0..1..0..1. .0..1..0..0
..1..1..1..1. .1..1..0..0. .0..0..0..0. .1..0..1..1. .1..1..0..0
..0..0..1..1. .1..1..0..0. .0..0..1..1. .0..0..1..0. .1..1..0..0
..0..0..1..1. .1..1..1..1. .1..1..0..0. .1..1..0..0. .1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A301999.

Empirical: a(n) = 4*a(n-1) -4*a(n-2) +a(n-3)

A301996 Number of nX5 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 18, 84, 468, 2856, 17800, 110036, 674984, 4130664, 25284068, 154853080, 948637896, 5811528980, 35601208264, 218086661704, 1335953081860, 8183781374680, 50132301702344, 307101237458324, 1881245567361512

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Column 5 of A301999.

			Some solutions for n=5
..0..0..0..0..0. .0..0..1..1..0. .0..0..1..1..1. .0..0..1..0..0
..1..1..1..1..0. .1..1..1..0..1. .0..0..0..0..1. .0..1..0..0..0
..0..0..1..0..0. .1..0..1..1..1. .1..1..1..1..0. .1..1..0..1..1
..0..1..1..1..0. .0..0..1..0..1. .0..0..0..0..0. .0..0..1..0..0
..0..0..1..0..0. .0..0..0..1..1. .1..1..0..1..1. .1..1..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A301999.

Empirical: a(n) = 18*a(n-1) -141*a(n-2) +661*a(n-3) -2058*a(n-4) +4393*a(n-5) -6412*a(n-6) +6060*a(n-7) -3280*a(n-8) +640*a(n-9) +192*a(n-10) -64*a(n-11) for n>12

A301997 Number of nX6 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 50, 309, 2036, 14016, 100176, 729297, 5333386, 39000114, 285003038, 2082142574, 15211180773, 111130989409, 811933398770, 5932115487834, 43341007947078, 316656251375882, 2313539966133653, 16903085362643740, 123496604929203700

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Column 6 of A301999.

			Some solutions for n=5
..0..0..0..1..0..0. .0..0..0..0..1..0. .0..0..1..1..0..1. .0..0..1..1..0..0
..1..1..1..0..0..0. .1..1..0..1..0..0. .0..0..1..0..1..1. .0..0..1..0..1..1
..0..0..1..0..0..0. .1..1..0..1..1..1. .0..0..1..0..0..0. .1..1..1..0..0..0
..1..1..1..0..1..1. .0..0..0..0..0..0. .0..1..1..1..1..1. .1..0..1..1..1..1
..1..1..0..1..0..0. .0..1..1..1..1..1. .0..0..0..0..1..1. .0..0..0..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A301999.

Empirical: a(n) = 37*a(n-1) -646*a(n-2) +7145*a(n-3) -56474*a(n-4) +340368*a(n-5) -1627864*a(n-6) +6344426*a(n-7) -20530229*a(n-8) +55921932*a(n-9) -129560648*a(n-10) +257379094*a(n-11) -441218290*a(n-12) +656019085*a(n-13) -849333774*a(n-14) +960248209*a(n-15) -949688428*a(n-16) +822086289*a(n-17) -622603894*a(n-18) +412123821*a(n-19) -238125530*a(n-20) +119900686*a(n-21) -52488320*a(n-22) +19925276*a(n-23) -6551781*a(n-24) +1868622*a(n-25) -461972*a(n-26) +97988*a(n-27) -17522*a(n-28) +2597*a(n-29) -306*a(n-30) +25*a(n-31) -a(n-32) for n>33

A301998 Number of nX7 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 128, 1108, 10982, 122232, 1366374, 15243860, 169636124, 1884309898, 20919022400, 232254936138, 2579000358404, 28639373845122, 318037976285038, 3531770886607536, 39219734913406306, 435528277377832336

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Column 7 of A301999.

			Some solutions for n=5
..0..0..1..0..1..0..0. .0..0..1..1..1..1..0. .0..0..1..0..0..1..1
..0..1..0..1..0..1..1. .0..0..0..0..1..0..1. .0..1..1..0..1..0..0
..1..0..0..1..0..1..0. .1..1..0..1..0..1..0. .0..0..1..1..0..1..1
..1..1..1..0..1..0..0. .1..1..0..1..1..0..1. .1..1..0..1..0..0..0
..0..0..0..1..1..1..1. .0..0..1..0..0..1..1. .0..0..1..1..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 52

Cf. A301999.

Empirical recurrence of order 52 (see link above)

A302000 Number of 3Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 5, 5, 26, 84, 309, 1108, 3979, 14314, 51440, 185083, 665473, 2393298, 8606453, 30950505, 111303112, 400265922, 1439423515, 5176415456, 18615274437, 66943726862, 240741120250, 865746384343, 3113372499381, 11196221683404

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Row 3 of A301999.

			Some solutions for n=5
..0..0..1..1..1. .0..0..0..1..1. .0..0..1..1..1. .0..0..0..1..1
..0..0..0..0..1. .1..1..1..0..1. .0..1..0..0..0. .1..1..0..1..1
..1..1..0..1..1. .0..0..0..1..1. .1..1..1..1..1. .1..0..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A301999.

Empirical: a(n) = 2*a(n-1) +6*a(n-2) -2*a(n-4) +2*a(n-5) -9*a(n-6) -50*a(n-7) -37*a(n-8) +34*a(n-9) +43*a(n-10) -16*a(n-11) +15*a(n-12) +18*a(n-13) -7*a(n-14) -2*a(n-16) +4*a(n-17) -6*a(n-18) +a(n-20)

A302001 Number of 4Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 13, 15, 74, 468, 2036, 10982, 53440, 271596, 1360466, 6832459, 34345485, 172485648, 866676017, 4353899691, 21873626234, 109891360736, 552080909728, 2773601514082, 13934283247296, 70004406947220, 351694969884786

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Row 4 of A301999.

			Some solutions for n=5
..0..0..1..1..0. .0..0..1..1..0. .0..0..1..1..0. .0..0..1..1..0
..0..0..0..0..0. .1..1..1..0..0. .0..0..1..0..1. .0..0..1..0..0
..1..1..0..1..1. .1..0..1..1..1. .0..1..0..1..0. .0..1..1..0..1
..1..1..1..0..0. .0..1..0..0..0. .1..0..1..0..0. .0..0..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A301999.

A302002 Number of 5Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 34, 48, 200, 2856, 14016, 122232, 813704, 6066698, 43025282, 311301306, 2237774274, 16116010598, 116014746014, 835190383512, 6012793756932, 43286754359604, 311629669798802, 2243474218816140, 16151152920460132

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Row 5 of A301999.

			Some solutions for n=5
..0..0..0..0..0. .0..0..1..0..0. .0..0..0..1..1. .0..0..1..1..0
..1..1..1..0..0. .1..1..1..1..0. .1..1..0..1..0. .0..1..1..0..1
..0..0..1..1..1. .1..0..1..0..0. .0..0..1..0..0. .0..0..1..1..1
..1..1..0..0..0. .0..1..1..0..0. .1..1..1..0..1. .0..0..1..0..1
..0..0..1..1..1. .0..0..1..1..1. .1..1..0..1..1. .1..1..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A301999.

A302003 Number of 6Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 89, 155, 530, 17800, 100176, 1366374, 12824770, 133115004, 1366157014, 13941336537, 143149041167, 1463519003210, 14995308550903, 153525291778069, 1572142108724428, 16098534802420026, 164847528194904576

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Row 6 of A301999.

			Some solutions for n=5
..0..0..1..1..1. .0..0..0..0..1. .0..0..0..0..1. .0..0..1..0..0
..0..0..0..1..0. .1..1..0..1..1. .1..1..0..1..0. .0..1..1..1..0
..1..1..1..0..1. .0..0..0..1..1. .0..0..1..0..1. .0..0..0..0..0
..0..0..1..1..1. .0..0..0..1..0. .1..1..0..1..1. .1..1..0..1..1
..0..0..1..0..0. .0..1..1..0..1. .0..0..0..1..0. .1..1..1..0..1
..0..0..0..1..1. .1..0..0..1..1. .0..1..1..0..0. .0..0..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A301999.

A302004 Number of 7Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 233, 499, 1394, 110036, 729297, 15243860, 204666568, 2933712940, 44201068772, 631467436258, 9310616032492, 135219892970154, 1977188363830961, 28827781254085548, 420748594948205104, 6138969205830064789

Offset: 1

R. H. Hardin, Mar 30 2018

nonn

Row 7 of A301999.

			Some solutions for n=5
..0..0..1..1..0. .0..0..1..1..0. .0..0..0..0..1. .0..0..0..1..1
..0..1..0..0..0. .0..0..0..0..0. .1..1..1..1..1. .1..1..1..0..0
..1..1..0..1..1. .1..1..0..1..1. .0..0..1..0..0. .0..0..1..1..0
..1..0..1..1..1. .1..1..0..0..1. .0..1..1..0..1. .0..0..1..0..1
..0..0..1..0..0. .0..0..0..1..1. .0..0..0..1..1. .0..0..0..1..1
..1..1..1..1..1. .0..1..0..1..1. .1..1..0..1..1. .1..1..0..0..0
..1..0..0..0..0. .1..0..0..0..0. .1..0..0..0..0. .1..0..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A301999.

cp's OEIS Frontend

A301994 Number of n X 3 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301995 Number of nX4 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301996 Number of nX5 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301997 Number of nX6 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301998 Number of nX7 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A302000 Number of 3Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A302001 Number of 4Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A302002 Number of 5Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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Author

Keywords

Comments

Examples

Links

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A302003 Number of 6Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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Author

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Comments

Examples

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A302004 Number of 7Xn 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.