A217982 -id:A217982 - cp's OEIS frontend

A217978 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 n X 4 array.

6, 6, 36, 98, 362, 1180, 4046, 13594, 46052, 155494, 525730, 1776548, 6004634, 20293538, 68587432, 231806206, 783444274, 2647830256, 8948960354, 30245088582, 102220312680, 345477304222, 1167620873294, 3946246173440, 13337256366382

Offset: 1

R. H. Hardin, Oct 16 2012

nonn

Column 4 of A217982.

			Some solutions for n=3:
..1..1..0..0....0..0..0..1....1..1..1..1....0..0..1..1....1..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..0
..0..0..1..1....1..0..0..0....0..0..0..1....1..0..0..0....0..0..0..0

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

Cf. A217982.

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) + a(n-3) - 5*a(n-4) - 8*a(n-5) + a(n-6) + 2*a(n-7).

Empirical g.f.: 2*x*(3 - 3*x - 3*x^2 - 5*x^3 + 5*x^4 + 4*x^5) / (1 - 2*x - 5*x^2 - x^3 + 5*x^4 + 8*x^5 - x^6 - 2*x^7). - Colin Barker, Jul 23 2018

A217979 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 nX5 array.

Original entry on oeis.org

10, 10, 100, 362, 1942, 8872, 43258, 205446, 986288, 4714274, 22573862, 108013892, 516992146, 2474201538, 11841537864, 56672476422, 271231398802, 1298094250056, 6212595977182, 29733069165822, 142300516403984, 681040858862718

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Column 5 of A217982

			Some solutions for n=3
..1..1..1..0..0....1..1..0..0..0....1..1..0..0..0....1..0..0..0..0
..0..0..1..0..0....1..0..0..0..0....1..0..0..0..0....1..0..0..0..0
..0..0..1..1..1....1..0..0..0..0....1..0..0..0..1....1..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..53

Empirical: a(n) = 3*a(n-1) +10*a(n-2) +a(n-3) -28*a(n-4) -58*a(n-5) +41*a(n-6) +39*a(n-7) -50*a(n-8) -9*a(n-9) +100*a(n-10) +368*a(n-11) -439*a(n-12) -51*a(n-13) +370*a(n-14) -249*a(n-15) -56*a(n-16) +106*a(n-17) -33*a(n-18) -7*a(n-19) +6*a(n-20) +a(n-21)

A217980 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 nX6 array.

Original entry on oeis.org

16, 16, 256, 1180, 8872, 54504, 363728, 2347480, 15361400, 99957900, 651962620, 4248252712, 27693131900, 180493901576, 1176474695224, 7668147995040, 49980828130368, 325772423519628, 2123371872316720, 13840043094715540

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Column 6 of A217982

			Some solutions for n=3
..1..1..0..0..0..1....0..0..0..0..0..1....1..1..0..0..0..1....1..1..0..0..0..0
..0..0..0..0..0..0....0..0..0..0..0..1....1..1..0..0..0..0....0..0..0..0..0..0
..0..0..1..1..0..0....0..0..0..0..0..1....1..1..1..0..0..0....0..0..1..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..101

Empirical: a(n) = 5*a(n-1) +20*a(n-2) -26*a(n-3) -243*a(n-4) -402*a(n-5) +1359*a(n-6) +3862*a(n-7) +575*a(n-8) -14159*a(n-9) -23730*a(n-10) +21635*a(n-11) +49428*a(n-12) +39959*a(n-13) -70045*a(n-14) -163116*a(n-15) +162408*a(n-16) +246212*a(n-17) -242465*a(n-18) -333744*a(n-19) +159949*a(n-20) +337852*a(n-21) -38088*a(n-22) -156828*a(n-23) -5419*a(n-24) +49017*a(n-25) +4621*a(n-26) -24626*a(n-27) -9053*a(n-28) +3845*a(n-29) +4770*a(n-30) +619*a(n-31) -302*a(n-32) -153*a(n-33) -20*a(n-34) +12*a(n-35)

A217981 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 nX7 array.

Original entry on oeis.org

26, 26, 676, 4046, 43258, 363728, 3375350, 30097566, 272859916, 2457033362, 22187715406, 200128757472, 1805997462058, 16294400662942, 147026523230292, 1326594311794394, 11969797169381830, 108002268912887340

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Column 7 of A217982

			Some solutions for n=3
..0..0..0..1..1..0..0....1..1..1..0..0..0..1....0..0..0..0..0..0..1
..0..0..0..0..0..0..0....1..1..1..0..0..0..1....0..0..0..0..0..0..0
..1..0..0..0..0..1..1....1..1..1..0..0..0..1....0..0..0..1..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..63

A217977 Number of n X n arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 n X n array.

Original entry on oeis.org

2, 2, 16, 98, 1942, 54504, 3375350, 368335390, 79138501972, 31734389399738, 24359808536352098, 35370314418915229140

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Diagonal of A217982

			Some solutions for n=3
..0..0..0....0..0..0....0..0..0....0..0..1....1..0..0....1..1..1....0..0..1
..0..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1....0..0..0
..1..1..1....0..0..0....1..0..0....0..0..1....0..0..0....0..0..1....1..0..0

cp's OEIS Frontend

A217978 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 n X 4 array.

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A217979 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 nX5 array.

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A217980 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 nX6 array.

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A217981 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 nX7 array.

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A217977 Number of n X n arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 n X n array.

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