A301615 -id:A301615 - cp's OEIS frontend

A301610 Number of nX3 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

1, 11, 62, 367, 2131, 12467, 72758, 425003, 2481842, 14494425, 84647239, 494344466, 2886987133, 16860117364, 98463698698, 575031667957, 3358206190785, 19612048586036, 114535089777733, 668889165654501, 3906337494564368

Offset: 1

R. H. Hardin, Mar 24 2018

nonn

Column 3 of A301615.

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

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

Cf. A301615.

Empirical: a(n) = 4*a(n-1) +12*a(n-2) -5*a(n-3) -14*a(n-4) +14*a(n-6) +4*a(n-7) -3*a(n-8) -5*a(n-9) +a(n-10)

A301611 Number of nX4 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

2, 34, 367, 3816, 40085, 421025, 4422826, 46459647, 488047397, 5126802206, 53855652961, 565739028561, 5942934438842, 62428910463417, 655798724558441, 6888987247456952, 72366937453302201, 760194996499019669

Offset: 1

R. H. Hardin, Mar 24 2018

nonn

Column 4 of A301615.

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

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

Cf. A301615.

Empirical: a(n) = 7*a(n-1) +41*a(n-2) -12*a(n-3) -318*a(n-4) -262*a(n-5) +724*a(n-6) +1034*a(n-7) -1340*a(n-8) -3422*a(n-9) +4016*a(n-10) +12158*a(n-11) +6925*a(n-12) -17989*a(n-13) -30269*a(n-14) +7574*a(n-15) +1694*a(n-16) +8004*a(n-17) -672*a(n-18) +432*a(n-19) -864*a(n-20) for n>21

A301612 Number of nX5 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 111, 2131, 40085, 758338, 14345706, 271301458, 5131197358, 97045266159, 1835413254015, 34712996298775, 656524254453280, 12416789603607923, 234837748693978527, 4441467446525879000, 84001117092821240904

Offset: 1

R. H. Hardin, Mar 24 2018

nonn

Column 5 of A301615.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 68

Cf. A301615.

Empirical recurrence of order 68 (see link above)

A301613 Number of nX6 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 361, 12467, 421025, 14345706, 488491106, 16632517333, 566336198475, 19283659583317, 656605634861657, 22357328417975688, 761263743052450453, 25920919868772588676, 882603544282198427622, 30052522164474593294535

Offset: 1

R. H. Hardin, Mar 24 2018

nonn

Column 6 of A301615.

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

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

Cf. A301615.

A301614 Number of nX7 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 1172, 72758, 4422826, 271301458, 16632517333, 1019565752074, 62500458737127, 3831336753439723, 234864521959895889, 14397413152054371201, 882574864133207632568, 54102660842288578973363, 3316543531108585833444946

Offset: 1

R. H. Hardin, Mar 24 2018

nonn

Column 7 of A301615.

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

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

Cf. A301615.

A301609 Number of n X n 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 3, 62, 3816, 758338, 488491106, 1019565752074, 6897694015722898, 151249886315100454600, 10749578188598491367494716

Offset: 1

R. H. Hardin, Mar 24 2018

nonn

Diagonal of A301615.

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

Cf. A301615.

cp's OEIS Frontend

A301610 Number of nX3 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

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A301611 Number of nX4 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

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A301612 Number of nX5 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

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A301613 Number of nX6 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

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A301614 Number of nX7 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

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A301609 Number of n X n 0..1 arrays with every element equal to 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

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