A300372 -id:A300372 - cp's OEIS frontend

A300367 Number of nX3 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 3, 3, 8, 16, 32, 70, 135, 293, 585, 1221, 2496, 5156, 10609, 21818, 44955, 92476, 190459, 391929, 806935, 1660946, 3419147, 7038323, 14488296, 29824518, 61393333, 126379174, 260151058, 535522942, 1102374986, 2269243610, 4671246404

Offset: 1

R. H. Hardin, Mar 04 2018

nonn

Column 3 of A300372.

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

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

Cf. A300372.

Empirical: a(n) = a(n-2) +2*a(n-3) +5*a(n-4) +6*a(n-5) +4*a(n-6) +6*a(n-7) +a(n-8) -a(n-12) +2*a(n-13) -a(n-14)

A300368 Number of nX4 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 3, 3, 4, 22, 39, 102, 298, 833, 2105, 6065, 16665, 45374, 126224, 348868, 962054, 2662783, 7364465, 20366371, 56334291, 155844294, 431150954, 1192657061, 3299782775, 9128883051, 25255840216, 69873935349, 193313945656, 534830511278

Offset: 1

R. H. Hardin, Mar 04 2018

nonn

Column 4 of A300372.

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

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

Cf. A300372.

Empirical: a(n) = 4*a(n-2) +8*a(n-3) +8*a(n-4) +12*a(n-5) -44*a(n-7) -152*a(n-8) -241*a(n-9) -140*a(n-10) -68*a(n-11) -156*a(n-12) +283*a(n-13) +514*a(n-14) +1368*a(n-15) +980*a(n-16) +28*a(n-17) -659*a(n-18) -792*a(n-19) -790*a(n-20) -705*a(n-21) -657*a(n-22) +8*a(n-23) +390*a(n-24) +453*a(n-25) -341*a(n-26) +569*a(n-27) -377*a(n-28) +201*a(n-29) -183*a(n-30) -139*a(n-31) +314*a(n-32) -196*a(n-33) +10*a(n-34) +78*a(n-35) -34*a(n-36) +2*a(n-37) -24*a(n-38) +52*a(n-39) -52*a(n-40) +28*a(n-41) -8*a(n-42) +a(n-43) for n>45

A300369 Number of nX5 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 3, 3, 4, 32, 92, 270, 1262, 3561, 13976, 48859, 173602, 622502, 2233811, 7882027, 28343929, 100832747, 360076171, 1284751998, 4584944102, 16356781324, 58381988677, 208293028674, 743376640816, 2652427350327, 9465170814378

Offset: 1

R. H. Hardin, Mar 04 2018

nonn

Column 5 of A300372.

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

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

Cf. A300372.

A300370 Number of nX6 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 2, 8, 22, 92, 366, 1592, 6925, 36101, 161645, 762469, 3571297, 16723114, 78166439, 365870424, 1715599255, 8028145462, 37613414368, 176081584796, 824491774631, 3861712572473, 18083391708768, 84680125527458, 396550577930555

Offset: 1

R. H. Hardin, Mar 04 2018

nonn

Column 6 of A300372.

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

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

Cf. A300372.

A300371 Number of nX7 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 6, 16, 39, 270, 1592, 12042, 75739, 490425, 3084820, 19634393, 129519588, 829432020, 5341866361, 34667291397, 223006749453, 1438573920539, 9290258941352, 59927615962595, 386783857393798, 2495707675837699

Offset: 1

R. H. Hardin, Mar 04 2018

nonn

Column 7 of A300372.

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

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

Cf. A300372.

A300366 Number of n X n 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 0, 3, 32, 366, 12042, 729062, 70536528, 13229207915, 4795249162868

Offset: 1

R. H. Hardin, Mar 04 2018

nonn

Diagonal of A300372.

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

Cf. A300372.

cp's OEIS Frontend

A300367 Number of nX3 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A300368 Number of nX4 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A300369 Number of nX5 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A300370 Number of nX6 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A300371 Number of nX7 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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A300366 Number of n X n 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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