A240327 -id:A240327 - cp's OEIS frontend

A240322 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

2, 5, 17, 37, 80, 213, 443, 1028, 2511, 5370, 12742, 29737, 65687, 155443, 355668, 803696, 1883007, 4285398, 9805203, 22760901, 51853646, 119272787, 275149593, 628629688, 1447871151, 3328934761, 7625189365, 17555754237, 40308328871

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

			Some solutions for n=4:
..3..2....3..2....3..2....3..2....3..2....2..3....2..3....2..3....2..3....2..3
..2..1....2..1....2..3....2..1....2..1....3..2....3..0....3..0....3..0....3..0
..3..1....2..0....3..2....3..2....3..0....2..3....3..2....3..1....2..1....3..1
..2..1....2..0....2..1....3..2....3..2....2..1....3..2....3..1....2..1....2..3

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

Column 2 of A240327.

Empirical: a(n) = 2*a(n-2) + 10*a(n-3) - a(n-4) - 5*a(n-5) - 15*a(n-6) + a(n-7) + 4*a(n-8) + 2*a(n-9) + 10*a(n-10) + 5*a(n-11) - 6*a(n-13) for n>14.

Empirical g.f.: x*(2 + 5*x + 13*x^2 + 7*x^3 - 2*x^4 - 16*x^5 - 15*x^6 - 3*x^7 + 2*x^8 + 11*x^9 + 13*x^10 + 3*x^11 - 3*x^12 - 4*x^13) / (1 - 2*x^2 - 10*x^3 + x^4 + 5*x^5 + 15*x^6 - x^7 - 4*x^8 - 2*x^9 - 10*x^10 - 5*x^11 + 6*x^13). - Colin Barker, Oct 27 2018

A240323 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

4, 17, 116, 455, 1677, 8091, 28448, 117304, 513841, 1871262, 7963314, 32859835, 125032724, 531287384, 2129046798, 8380565700, 35092450158, 139319279619, 559869375850, 2308650810237, 9177286253390, 37241010454269, 151821739788451

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 3 of A240327

			Some solutions for n=4
..3..2..3....3..2..2....3..2..2....2..3..3....3..2..3....2..3..2....2..3..3
..2..1..1....2..1..1....2..3..0....3..1..2....2..1..1....3..1..3....3..0..1
..3..0..2....3..0..0....3..2..0....3..1..3....3..2..2....3..1..2....2..1..1
..3..2..0....2..1..2....3..2..0....2..3..2....2..3..0....3..2..2....2..1..0

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

A240324 Number of nX4 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

6, 37, 455, 3374, 21455, 189549, 1190246, 8903613, 70945972, 460466581, 3565876476, 26437586127, 180411185989, 1394924206374, 9999389423346, 71022206087648, 538759260350717, 3826996325512698, 27847080935840982

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 4 of A240327

			Some solutions for n=4
..3..2..3..3....3..2..2..2....2..3..3..2....2..3..2..2....3..2..3..3
..2..3..2..2....2..1..1..1....3..1..1..3....3..1..3..1....2..1..2..2
..3..0..0..2....3..0..0..2....3..2..3..2....3..1..2..1....3..0..0..0
..3..2..2..2....2..1..1..3....2..1..1..1....3..2..0..3....2..1..0..0

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

A240325 Number of n X 5 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

8, 80, 1677, 21455, 247187, 3898804, 43979526, 602874070, 8649395684, 101952716878, 1438937234148, 19175029391887, 237935384258519, 3335405244297922, 43049779553837333, 556801688251633585

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 5 of A240327.

			Some solutions for n=4
..3..2..2..2..3....2..3..2..2..3....3..2..3..2..3....3..2..3..3..2
..2..3..0..0..0....3..1..1..0..0....2..3..0..3..2....2..3..2..2..3
..2..0..1..1..2....3..2..2..0..2....3..2..2..2..0....3..2..0..0..3
..2..0..1..2..3....2..3..0..3..3....2..1..0..2..3....3..1..3..2..3

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

Cf. A240327.

A240326 Number of nX6 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

14, 213, 8091, 189549, 3898804, 113751796, 2343565571, 58754628922, 1550370290554, 33299137997969, 861337519232031, 21016117833481545, 474930037525217349, 12220742975175544998, 287468219917419510614

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 6 of A240327

			Some solutions for n=3
..2..3..2..2..3..3....2..3..2..2..3..3....3..2..3..3..2..3....2..3..3..2..3..3
..3..2..3..1..2..2....3..1..3..0..2..2....2..1..1..2..3..2....3..1..1..3..2..1
..3..2..0..2..2..2....3..1..2..1..0..0....3..1..2..3..0..0....2..1..2..2..0..2

R. H. Hardin, Table of n, a(n) for n = 1..18

cp's OEIS Frontend

A240322 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240323 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240324 Number of nX4 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240325 Number of n X 5 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240326 Number of nX6 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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