A240046 -id:A240046 - cp's OEIS frontend

A240041 Number of nX2 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 zero 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, 4, 10, 22, 50, 119, 276, 637, 1473, 3355, 7682, 17497, 39777, 90406, 205111, 465359, 1054871, 2390302, 5415591, 12265608, 27777095, 62895884, 142401878, 322392952, 729835421, 1652150714, 3739914222, 8465684665, 19162662378, 43375394510

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Column 2 of A240046

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

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

Empirical: a(n) = 3*a(n-2) +10*a(n-3) +3*a(n-4) -12*a(n-5) -46*a(n-6) -36*a(n-7) +12*a(n-8) +107*a(n-9) +87*a(n-10) +2*a(n-11) -145*a(n-12) -138*a(n-13) -48*a(n-14) +147*a(n-15) +185*a(n-16) +89*a(n-17) -94*a(n-18) -210*a(n-19) -111*a(n-20) +40*a(n-21) +176*a(n-22) +85*a(n-23) +30*a(n-24) -77*a(n-25) -47*a(n-26) -57*a(n-27) +14*a(n-29) +21*a(n-30) +14*a(n-31) -3*a(n-32) +2*a(n-33) -5*a(n-34) +a(n-35) +2*a(n-36) +a(n-37) -a(n-38) for n>40

A240042 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 zero 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, 26, 93, 309, 1043, 3597, 12865, 45491, 163686, 584594, 2103512, 7548847, 27174662, 97768996, 352008043, 1267200666, 4563053012, 16431815183, 59173883901, 213095423135, 767419010967, 2763770574117, 9953309109574

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Column 3 of A240046

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

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

A240043 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 zero 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, 20, 72, 346, 1496, 8567, 46381, 268672, 1556758, 9438166, 56174788, 346760638, 2098659043, 13032771483, 79558734990, 494814764391, 3034462087200, 18868201942704, 116012171614159, 720835003158134, 4439604572498702

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Column 4 of A240046

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

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

A240047 Number of 2Xn 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 zero 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, 4, 9, 20, 33, 76, 117, 232, 398, 675, 1228, 2002, 3548, 5935, 10128, 17287, 28967, 49649, 83130, 141412, 238567, 402406, 681948, 1147552, 1943230, 3275448, 5532679, 9343794, 15759620, 26629572, 44915334, 75854561, 128021118, 216075045

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Row 2 of A240046

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

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

Empirical: a(n) = 3*a(n-2) +4*a(n-3) -3*a(n-4) -7*a(n-5) -5*a(n-6) +6*a(n-7) +4*a(n-8) +a(n-9) -3*a(n-10) +2*a(n-11) -a(n-12) -2*a(n-14) +4*a(n-15) -2*a(n-18) for n>22

A240048 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 zero 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, 10, 26, 72, 174, 597, 1187, 3115, 7269, 16520, 39181, 89951, 210684, 483773, 1131924, 2616441, 6047969, 14112456, 32543109, 75591535, 175328537, 405822918, 941534652, 2181820138, 5057085795, 11720944941, 27171466826, 62973901722

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Row 3 of A240046

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

R. H. Hardin, Table of n, a(n) for n = 1..200
R. H. Hardin, Empirical recurrence of order 76

Empirical recurrence of order 76 (see link above)

A240049 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 zero 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, 22, 93, 346, 1110, 5780, 17297, 57800, 202995, 643326, 2233216, 7442776, 25047361, 84213282, 278643460, 939079721, 3094143301, 10358660848, 34579518631, 114236046070, 383085583978, 1270523789559, 4220562761492

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Row 4 of A240046

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

R. H. Hardin, Table of n, a(n) for n = 1..166

A240050 Number of 5 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 zero 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, 50, 309, 1496, 7514, 55034, 236282, 1248277, 6431987, 29170979, 155931126, 801190472, 4068998418, 19619747500, 103973075128, 508889855031, 2476317886402, 12705627199443, 63280997191424, 313215400063102

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Row 5 of A240046.

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

R. H. Hardin, Table of n, a(n) for n = 1..23

Cf. A240046.

A240040 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 zero 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, 4, 26, 346, 7514, 640643, 104619164, 49892724623

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Diagonal of A240046

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

A240044 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 zero 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, 33, 174, 1110, 7514, 61858, 515675, 4743056, 45158204, 453408919, 4712861517, 51120946600, 562235041667, 6362903006738, 71977060151899, 829848814960705, 9503133899373343, 110368341821576074

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Column 5 of A240046

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

A240045 Number of n X 6 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 zero 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

14, 76, 597, 5780, 55034, 640643, 8300260, 119956268, 1944727891, 34311716212, 646898229040

Offset: 1

R. H. Hardin, Mar 31 2014

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

Column 6 of A240046.

cp's OEIS Frontend

A240041 Number of nX2 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 zero 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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A240042 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 zero 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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A240043 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 zero 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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A240047 Number of 2Xn 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 zero 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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A240048 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 zero 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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A240049 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 zero 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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A240050 Number of 5 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 zero 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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A240040 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 zero 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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A240044 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 zero 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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A240045 Number of n X 6 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 zero 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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