A241283 -id:A241283 - cp's OEIS frontend

A241278 Number of nX2 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

3, 3, 9, 36, 139, 532, 2111, 8473, 34053, 136880, 550213, 2211810, 8891567, 35744766, 143696235, 577666729, 2322248891, 9335550407, 37529342193, 150869654682, 606502776180, 2438168211361, 9801544653549, 39402644818707, 158400380771179

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Column 2 of A241283

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

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

Empirical: a(n) = 8*a(n-1) -20*a(n-2) +16*a(n-3) +4*a(n-4) -25*a(n-5) +53*a(n-6) -68*a(n-7) +100*a(n-8) -62*a(n-9) -41*a(n-10) +34*a(n-11) -117*a(n-12) +108*a(n-13) -54*a(n-14) +93*a(n-15) +41*a(n-16) +20*a(n-17) +8*a(n-18) -41*a(n-19) -26*a(n-20) -41*a(n-21) +9*a(n-22) +5*a(n-23) +2*a(n-24) +4*a(n-25) -13*a(n-26) +4*a(n-27) -3*a(n-28) -2*a(n-29) +4*a(n-30) +a(n-31)

A241279 Number of n X 3 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

4, 5, 41, 236, 1615, 12356, 96171, 761754, 6079503, 48655224, 389953075, 3127470262, 25091008666, 201333623389, 1615666305519, 12966002651979, 104056784269403, 835102517412497, 6702114259119338, 53787979810054439

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Column 3 of A241283.

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

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

Cf. A241283.

A241280 Number of nX4 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

7, 13, 126, 773, 6783, 77955, 1009773, 14440961, 217830879, 3381893022, 53303588755, 846694715304, 13502819912939, 215775668844659, 3451661371624419, 55243520432395260, 884402593677949937

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Column 4 of A241283

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

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

A241284 Number of 2Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

4, 3, 5, 13, 17, 35, 90, 141, 288, 670, 1101, 2265, 4995, 8474, 17477, 37329, 64894, 133967, 279966, 496683, 1023868, 2105032, 3799717, 7810452, 15858460, 29052053, 59504463, 119660776, 221989407, 452920894, 904106577, 1695187559, 3445124586

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Row 2 of A241283

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

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

Empirical: a(n) = a(n-1) +a(n-2) +7*a(n-3) -8*a(n-4) -7*a(n-5) +9*a(n-7) +10*a(n-8) -24*a(n-9) +5*a(n-10) +29*a(n-11) -18*a(n-12) -10*a(n-13) -10*a(n-14) +16*a(n-15) +12*a(n-16) -12*a(n-17) for n>18

A241285 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

10, 9, 41, 126, 224, 934, 2741, 5225, 20537, 55667, 113588, 422541, 1125360, 2473769, 8840311, 23068806, 53641026, 184488860, 476641936, 1157699906, 3848451987, 9887622772, 24862454468, 80220253420, 205811182949, 531847795781

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Row 3 of A241283

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

R. H. Hardin, Table of n, a(n) for n = 1..170

A241286 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

24, 36, 236, 773, 1800, 16843, 54167, 159403, 1014287, 3055986, 10609732, 60969600, 191316011, 725713555, 3761999379, 12377676801, 48908645074, 236055743934, 808188094976, 3233355467890, 14810044876373, 52228582550562

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Row 4 of A241283

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

R. H. Hardin, Table of n, a(n) for n = 1..148

A241287 Number of 5Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

56, 139, 1615, 6783, 20717, 451318, 1543713, 8288114, 79113707, 276340333, 1878731208, 14642190232, 59010752583, 404841299508, 2875913561864, 13757588225177, 90753330244908, 606550462257317, 3111205949073436

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Row 5 of A241283

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

R. H. Hardin, Table of n, a(n) for n = 1..20

A241277 Number of n X n 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 3, 41, 773, 20717, 15616828, 2949336562

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Diagonal of A241283

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

A241281 Number of nX5 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

10, 17, 224, 1800, 20717, 309657, 5423164, 113305157, 2759021846, 75062814060, 2194626322280, 66941258995665, 2089883847033445, 66049038598082087, 2100649576601196394, 67025504140569165794

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Column 5 of A241283

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

A241282 Number of nX6 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

15, 35, 934, 16843, 451318, 15616828, 730435588, 40083129145, 2390612565177, 147969997624544

Offset: 1

R. H. Hardin, Apr 18 2014

nonn

Column 6 of A241283

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

cp's OEIS Frontend

A241278 Number of nX2 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A241279 Number of n X 3 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A241280 Number of nX4 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A241284 Number of 2Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A241285 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A241286 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A241287 Number of 5Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A241277 Number of n X n 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A241281 Number of nX5 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A241282 Number of nX6 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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