A295213 -id:A295213 - cp's OEIS frontend

A295208 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.

1, 4, 10, 27, 102, 345, 1162, 4072, 14224, 49604, 173594, 607485, 2125150, 7436416, 26022865, 91060814, 318652127, 1115077417, 3902040209, 13654599697, 47782246634, 167206840944, 585115414586, 2047524354146, 7165006769433

Offset: 1

R. H. Hardin, Nov 17 2017

nonn

Column 3 of A295213.

			Some solutions for n=7
..1..1..1. .0..1..1. .0..1..1. .1..1..1. .0..1..1. .0..1..1. .1..1..0
..1..1..1. .0..1..1. .0..1..1. .1..0..1. .0..1..1. .0..1..1. .1..1..0
..1..0..1. .0..0..0. .0..1..0. .1..1..1. .0..1..1. .1..1..1. .1..0..0
..1..0..1. .1..1..0. .0..1..0. .1..1..0. .0..0..0. .1..0..1. .1..0..0
..1..1..1. .1..1..0. .1..1..0. .0..0..0. .0..0..0. .1..0..1. .1..1..0
..0..1..1. .1..1..0. .1..1..0. .1..1..1. .0..1..1. .1..1..1. .1..1..0
..0..0..0. .0..0..0. .1..1..0. .1..1..1. .0..1..1. .0..1..1. .0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210
Robert Israel, Maple-assisted proof of formula

Cf. A295213.

Empirical: a(n) = 5*a(n-1) -7*a(n-2) +10*a(n-3) -18*a(n-4) +18*a(n-5) -5*a(n-6) -15*a(n-7) +7*a(n-8) -9*a(n-9) +10*a(n-10) -2*a(n-11) +a(n-12).

Empirical formula confirmed by Robert Israel, Nov 17 2017 (see link).

A295209 Number of n X 4 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.

Original entry on oeis.org

1, 7, 27, 147, 916, 4938, 27208, 152236, 848992, 4746938, 26555583, 148468255, 830063597, 4640855585, 25946470239, 145065530889, 811058197498, 4534601269690, 25352811924120, 141746752099136, 792501412285360

Offset: 1

R. H. Hardin, Nov 17 2017

nonn

Column 4 of A295213.

			Some solutions for n=7
..0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..0..0. .0..1..1..1
..0..0..1..1. .1..0..1..1. .1..0..1..1. .1..1..1..0. .1..1..1..1
..0..0..1..1. .1..1..1..1. .1..1..0..0. .1..0..1..0. .1..0..0..0
..0..0..1..1. .0..1..0..0. .0..1..1..0. .1..0..1..0. .1..1..1..0
..1..1..1..1. .0..1..1..0. .0..0..1..0. .1..0..1..0. .1..1..1..0
..1..1..0..1. .0..1..1..0. .0..1..1..0. .1..1..1..0. .0..0..1..1
..0..1..1..1. .0..0..0..0. .0..1..1..0. .1..1..0..0. .0..0..1..1

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

Cf. A295213.

Empirical: a(n) = 8*a(n-1) -17*a(n-2) +27*a(n-3) -66*a(n-4) +182*a(n-5) -188*a(n-6) -199*a(n-7) -22*a(n-8) +185*a(n-9) +385*a(n-10) +169*a(n-11) +49*a(n-12) +408*a(n-13) +516*a(n-14) -492*a(n-15) -1779*a(n-16) -408*a(n-17) +326*a(n-18) -331*a(n-19) +505*a(n-20) -310*a(n-21) +217*a(n-22) -111*a(n-23) +4*a(n-24) -16*a(n-25) +4*a(n-26) +4*a(n-27) -a(n-28).

A295210 Number of nX5 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1s.

Original entry on oeis.org

1, 14, 102, 916, 9536, 85215, 775547, 7213161, 66719868, 617206899, 5712427735, 52846385777, 488921918232, 4523682017995, 41853575267115, 387232937869441, 3582725192257390, 33147778088300382, 306687046141834012

Offset: 1

R. H. Hardin, Nov 17 2017

nonn

Column 5 of A295213.

			Some solutions for n=6
..1..1..0..0..0. .1..1..1..1..1. .0..1..1..1..1. .1..1..1..1..1
..1..1..0..0..0. .1..1..0..1..1. .0..1..0..0..1. .1..0..0..1..1
..1..0..1..1..1. .1..0..0..1..1. .0..1..1..1..1. .1..1..1..1..0
..1..1..1..0..1. .1..0..0..1..1. .0..1..0..0..0. .1..0..1..1..0
..0..0..1..1..1. .1..1..0..1..0. .0..1..1..1..0. .1..1..0..0..0
..0..0..1..1..1. .1..1..1..1..0. .0..1..1..1..0. .1..1..0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 78

Cf. A295213.

Empirical recurrence of order 78 (see link above)

A295211 Number of nX6 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1s.

Original entry on oeis.org

1, 31, 345, 4938, 85215, 1245294, 18444470, 278238087, 4170628296, 62588525694, 940255638767, 14117945596996, 211965773459470, 3182555837979301, 47783850148231569, 717445698125438780, 10772054909227440585

Offset: 1

R. H. Hardin, Nov 17 2017

nonn

Column 6 of A295213.

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

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

Cf. A295213.

A295212 Number of nX7 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1s.

Original entry on oeis.org

1, 69, 1162, 27208, 775547, 18444470, 444447937, 10896495280, 265837272259, 6495847859424, 158822121967384, 3880909066698091, 94831337129003187, 2317336322758510242, 56626572178295328836, 1383738694001835856870

Offset: 1

R. H. Hardin, Nov 17 2017

nonn

Column 7 of A295213.

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

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

Cf. A295213.

A295207 Number of n X n 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.

Original entry on oeis.org

1, 2, 10, 147, 9536, 1245294, 444447937, 436106162865, 1123957773816109, 7694570450089060470, 140076394691747502547476

Offset: 1

R. H. Hardin, Nov 17 2017

nonn

Diagonal of A295213.

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

Cf. A295213.

cp's OEIS Frontend

A295208 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.

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A295209 Number of n X 4 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.

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A295210 Number of nX5 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1s.

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A295211 Number of nX6 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1s.

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A295212 Number of nX7 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1s.

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A295207 Number of n X n 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.

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