A240153 -id:A240153 - cp's OEIS frontend

A240148 Number of nX2 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

3, 5, 11, 25, 62, 144, 329, 775, 1781, 4150, 9625, 22243, 51656, 119768, 277454, 643440, 1492066, 3458520, 8019402, 18594916, 43110992, 99960080, 231775985, 537393625, 1246028348, 2889126804, 6698837457, 15532273640, 36014074118

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Column 2 of A240153

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

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

Empirical: a(n) = 3*a(n-2) +14*a(n-3) +5*a(n-4) -28*a(n-5) -89*a(n-6) -50*a(n-7) +93*a(n-8) +303*a(n-9) +214*a(n-10) -113*a(n-11) -561*a(n-12) -468*a(n-13) -47*a(n-14) +584*a(n-15) +499*a(n-16) +142*a(n-17) -359*a(n-18) -96*a(n-19) -23*a(n-20) +128*a(n-21) -102*a(n-22) -99*a(n-23) -119*a(n-24) +32*a(n-25) +82*a(n-26) +113*a(n-27) +50*a(n-28) -7*a(n-29) -42*a(n-30) -20*a(n-31) +a(n-32) +4*a(n-33) +a(n-34) for n>36

A240149 Number of nX3 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

4, 8, 20, 67, 254, 825, 2667, 8652, 27929, 91436, 297311, 965014, 3135633, 10174603, 33030794, 107154304, 347714014, 1127972498, 3659419980, 11870924983, 38508782933, 124917347816, 405214920992, 1314447547691, 4263837727610

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Column 3 of A240153

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

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

A240150 Number of nX4 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

7, 19, 107, 676, 3993, 22412, 131005, 731518, 4144347, 23263202, 131973267, 742448151, 4200516883, 23673251649, 133792056873, 754644250144, 4262766555182, 24053911144152, 135834058269434, 766651910127519

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Column 4 of A240153

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

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

A240154 Number of 2Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

3, 5, 8, 19, 36, 57, 120, 218, 377, 758, 1366, 2451, 4815, 8678, 15839, 30594, 55356, 102004, 194522, 353711, 655297, 1238182, 2261878, 4202427, 7889648, 14469040, 26917836, 50315864, 92567160, 172279431, 321102231, 592194036, 1102055156

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Row 2 of A240153

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

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

Empirical: a(n) = a(n-2) +8*a(n-3) -5*a(n-5) -18*a(n-6) +a(n-7) +10*a(n-8) +16*a(n-9) -5*a(n-10) -10*a(n-11) +a(n-12) +6*a(n-13) -2*a(n-14) -6*a(n-15) -a(n-16) +6*a(n-17) for n>19

A240155 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

4, 11, 20, 107, 186, 450, 1641, 2788, 8018, 23175, 45126, 134673, 357608, 737260, 2166386, 5505921, 11966760, 34560626, 85121623, 194751022, 548083132, 1325791556, 3156785846, 8660504920, 20790818391, 50929828270, 136560783094

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Row 3 of A240153

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

R. H. Hardin, Table of n, a(n) for n = 1..184

A240156 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

7, 25, 67, 676, 1328, 5701, 24419, 52676, 243555, 876504, 2400051, 10681824, 37465330, 108284648, 460964686, 1527396439, 4792821890, 19591078862, 63187977557, 212419410767, 830175708307, 2671224202187, 9338356637595

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Row 4 of A240153

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

R. H. Hardin, Table of n, a(n) for n = 1..155

A240157 Number of 5Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

10, 62, 254, 3993, 11742, 88214, 536744, 1652584, 11331387, 57296488, 223202826, 1550772274, 7551863892, 32607176000, 200353447144, 939471999117, 4301332018225, 25319460629707, 117174747947500, 578341876385557

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Row 5 of A240153

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

R. H. Hardin, Table of n, a(n) for n = 1..21

A240147 Number of n X n 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 5, 20, 676, 11742, 1608415, 417799464

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Diagonal of A240153

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

A240151 Number of nX5 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

10, 36, 186, 1328, 11742, 108201, 1056699, 10526838, 107361960, 1116331018, 11525618748, 120250941392, 1248359598803, 13042277879115, 135683637852581, 1417567382471017, 14760989837426228

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Column 5 of A240153

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

A240152 Number of nX6 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

15, 57, 450, 5701, 88214, 1608415, 30542203, 584983851, 11643589675, 228028231216

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Column 6 of A240153

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

cp's OEIS Frontend

A240148 Number of nX2 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A240149 Number of nX3 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A240150 Number of nX4 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A240154 Number of 2Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A240155 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A240156 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A240157 Number of 5Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A240147 Number of n X n 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A240151 Number of nX5 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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A240152 Number of nX6 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

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