A239858 -id:A239858 - cp's OEIS frontend

A239851 Number of n X 1 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

2, 2, 4, 6, 8, 14, 20, 30, 48, 70, 108, 166, 248, 382, 580, 878, 1344, 2038, 3100, 4726, 7176, 10926, 16628, 25278, 38480, 58534, 89036, 135494, 206104, 313566, 477092, 725774, 1104224, 1679958, 2555772, 3888406, 5915688, 8999950, 13692500

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

Column 1 of A239858.

			All solutions for n=4:
..3....3....2....2....2....3
..2....2....3....3....3....2
..3....3....3....2....3....2
..2....3....3....2....2....2

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

Empirical: a(n) = a(n-2) +2*a(n-3).

Empirical g.f.: 2*x*(1 + x + x^2) / (1 - x^2 - 2*x^3). - Colin Barker, Feb 18 2018

A239852 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 3, 5, 4, 5, 5, 6, 10, 11, 15, 16, 21, 26, 32, 41, 48, 62, 74, 94, 115, 142, 177, 216, 271, 331, 413, 508, 629, 779, 960, 1192, 1468, 1821, 2247, 2781, 3439, 4249, 5260, 6496, 8041, 9935, 12290, 15195, 18786, 23236, 28721, 35526, 43916, 54312, 67152, 83033

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

			All solutions for n=4:
..3..2....3..2....3..2....2..3
..2..3....2..3....2..3....3..0
..2..0....3..0....3..0....3..2
..2..0....2..3....3..2....2..3

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

Column 2 of A239858.

Empirical: a(n) = a(n-2) + a(n-5) for n>9.

Empirical g.f.: x*(2 + 3*x + 3*x^2 + x^3 - x^5 - 2*x^6 + x^8) / (1 - x^2 - x^5). - Colin Barker, Oct 26 2018

A239853 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

4, 9, 44, 84, 130, 343, 685, 1704, 3977, 7958, 18574, 40388, 86314, 203202, 433430, 967411, 2205109, 4735287, 10746065, 23937983, 52281965, 118605335, 261244402, 578751600, 1302168082, 2864205270, 6395152778, 14272351652, 31509181522

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

Column 3 of A239858

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

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

A239854 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

6, 12, 78, 203, 484, 1757, 4979, 19850, 68830, 207822, 799573, 2488921, 8261626, 29985170, 94570580, 336674607, 1151293607, 3775219224, 13467393979, 44587173533, 151997573760, 528796519331, 1751682284364, 6079087768020

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

Column 4 of A239858

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

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

A239855 Number of nX5 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

8, 29, 255, 1114, 4549, 28184, 125255, 860559, 4802971, 24477675, 167075425, 824227912, 4838346333, 28474926407, 141317949021, 883311612241, 4759951691561, 26045766222755, 156842648720379, 819459824961446

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

Column 5 of A239858

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

R. H. Hardin, Table of n, a(n) for n = 1..40

A239859 Number of 2 X n 0..3 arrays with no element equal to zero 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, 9, 12, 29, 63, 100, 215, 468, 785, 1654, 3515, 6048, 12676, 26381, 46460, 96810, 198286, 355994, 737992, 1493159, 2724777, 5619409, 11263131, 20836948, 42752798, 85081916, 159218104, 325067366, 643478067, 1215731399, 2470549558, 4871466920

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

Row 2 of A239858.

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

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

Cf. A239858.

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>21.

A239860 Number of 3Xn 0..3 arrays with no element equal to zero 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, 5, 44, 78, 255, 742, 1382, 5647, 14755, 33946, 120389, 305123, 717503, 2451925, 6276842, 15461619, 51283453, 130329061, 331984698, 1067700153, 2718467454, 7099921104, 22241389875, 56803646347, 151320850227, 463374925294

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

Row 3 of A239858

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

R. H. Hardin, Table of n, a(n) for n = 1..174

A239861 Number of 4Xn 0..3 arrays with no element equal to zero 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

6, 4, 84, 203, 1114, 3463, 9963, 71695, 219708, 889871, 4682227, 14101348, 56490669, 272270300, 908846318, 3737847138, 17250775307, 59577644920, 244962530289, 1088932223860, 3891762853661, 15991497390003, 68807314247286

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

Row 4 of A239858

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

R. H. Hardin, Table of n, a(n) for n = 1..151

A239862 Number of 5Xn 0..3 arrays with no element equal to zero 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

8, 5, 130, 484, 4549, 19065, 77212, 970717, 4024283, 29283865, 237306256, 903816798, 6001392838, 42830861947, 200921301635, 1351900199288, 8836338066911, 44530526981817, 287975221682482, 1867118985367733

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

Row 5 of A239858

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

R. H. Hardin, Table of n, a(n) for n = 1..22

A239850 Number of n X n 0..3 arrays with no element equal to zero 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, 44, 203, 4549, 176208, 9885999, 14757679494

Offset: 1

R. H. Hardin, Mar 28 2014

nonn

Diagonal of A239858

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

cp's OEIS Frontend

A239851 Number of n X 1 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A239852 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A239853 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A239854 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A239855 Number of nX5 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A239859 Number of 2 X n 0..3 arrays with no element equal to zero 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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A239860 Number of 3Xn 0..3 arrays with no element equal to zero 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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A239861 Number of 4Xn 0..3 arrays with no element equal to zero 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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A239862 Number of 5Xn 0..3 arrays with no element equal to zero 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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A239850 Number of n X n 0..3 arrays with no element equal to zero 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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