A241054 -id:A241054 - cp's OEIS frontend

A241050 Number of n X 2 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 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.

3, 3, 4, 6, 8, 12, 13, 20, 28, 38, 53, 68, 96, 130, 178, 245, 330, 454, 617, 841, 1153, 1563, 2144, 2913, 3982, 5431, 7404, 10111, 13783, 18809, 25665, 34995, 47772, 65135, 88894, 121250, 165416, 225685, 307854, 420020, 572988, 781677, 1066446, 1454794

Offset: 1

R. H. Hardin, Apr 15 2014

nonn

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

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

Column 2 of A241054.

Empirical: a(n) = 2*a(n-2) - a(n-4) + a(n-5) - a(n-7) + a(n-8) + a(n-11) for n>15.

Empirical g.f.: x*(3 + 3*x - 2*x^2 + 3*x^4 - 2*x^6 + x^7 + 4*x^8 + 3*x^9 - 2*x^11 - x^12 + x^13 + 2*x^14) / ((1 + x)*(1 - x - x^2 + x^3 - x^5 + x^6 - x^8 + x^9 - x^10)). - Colin Barker, Oct 29 2018

A241051 Number of nX3 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 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, 2, 3, 6, 6, 15, 31, 58, 170, 388, 677, 1821, 3533, 7379, 18106, 37073, 82436, 193696, 400749, 914323, 2049019, 4372160, 9966006, 21985585, 47864157, 108257464, 237088178, 522824937, 1171545248, 2567836513, 5698120668, 12680572718

Offset: 1

R. H. Hardin, Apr 15 2014

nonn

Column 3 of A241054

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

R. H. Hardin, Table of n, a(n) for n = 1..250

A241052 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 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

7, 10, 24, 64, 132, 690, 2142, 7144, 30662, 95669, 356203, 1295102, 4422715, 16996927, 58368376, 210047376, 778300845, 2685487991, 9897567452, 35427665822, 125536795397, 459821814155, 1627346610378, 5869761114047, 21203315127283

Offset: 1

R. H. Hardin, Apr 15 2014

nonn

Column 4 of A241054

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

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

A241053 Number of n X 5 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 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

10, 18, 60, 163, 598, 3411, 11283, 72578, 404421, 2220973, 15323311, 89098530, 555805615, 3439171493, 20036872248, 122952210402, 718794479207, 4313956945052, 26242676909613, 154481099979249, 936900491409907

Offset: 1

R. H. Hardin, Apr 15 2014

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

R. H. Hardin, Table of n, a(n) for n = 1..33

Column 5 of A241054.

A241055 Number of 2 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 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, 3, 2, 10, 18, 18, 46, 58, 102, 173, 264, 487, 738, 1318, 2151, 3591, 6192, 10096, 17480, 28925, 49131, 82966, 138977, 236535, 395979, 671706, 1131018, 1908201, 3226558, 5432423, 9189152, 15486612, 26156656, 44151446, 74485403, 125808822

Offset: 1

R. H. Hardin, Apr 15 2014

nonn

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

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

Row 2 of A241054.

Empirical: a(n) = 3*a(n-2) + 3*a(n-3) - 3*a(n-4) - 4*a(n-5) - 2*a(n-6) + 3*a(n-7) - a(n-9) + 2*a(n-11) - 2*a(n-12) + 2*a(n-15) for n>17.

Empirical g.f.: x*(2 + 3*x - 4*x^2 - 5*x^3 + 9*x^4 - x^5 - 16*x^6 - 12*x^7 - x^8 + 3*x^9 + 3*x^10 + 11*x^12 - 10*x^13 - 8*x^14 + 6*x^15 + 8*x^16) / ((1 - x)*(1 + x - 2*x^2 - 5*x^3 - 2*x^4 + 2*x^5 + 4*x^6 + x^7 + x^8 + 2*x^9 + 2*x^10 + 2*x^12 + 2*x^13 + 2*x^14)). - Colin Barker, Oct 29 2018

A241056 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 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, 4, 3, 24, 60, 93, 297, 507, 1264, 2850, 6180, 15453, 33463, 81394, 185671, 428769, 1005669, 2301449, 5384371, 12403537, 28828484, 66828140, 154614938, 359224400, 831157978, 1928175521, 4468984943, 10355201708, 24011010277, 55638167866

Offset: 1

R. H. Hardin, Apr 15 2014

nonn

Row 3 of A241054

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

R. H. Hardin, Table of n, a(n) for n = 1..201

Empirical: a(n) = 9*a(n-2) +12*a(n-3) -36*a(n-4) -94*a(n-5) +42*a(n-6) +366*a(n-7) +182*a(n-8) -847*a(n-9) -1102*a(n-10) +1053*a(n-11) +3109*a(n-12) +196*a(n-13) -5605*a(n-14) -4198*a(n-15) +6248*a(n-16) +11838*a(n-17) -1164*a(n-18) -20204*a(n-19) -9948*a(n-20) +22399*a(n-21) +20007*a(n-22) -15440*a(n-23) -32138*a(n-24) -3232*a(n-25) +46610*a(n-26) +38214*a(n-27) -37132*a(n-28) -43172*a(n-29) +14617*a(n-30) +32371*a(n-31) +36897*a(n-32) +8088*a(n-33) -123047*a(n-34) -63621*a(n-35) +134896*a(n-36) +125072*a(n-37) -107223*a(n-38) -179919*a(n-39) +66957*a(n-40) +285064*a(n-41) -143540*a(n-42) -368756*a(n-43) +184926*a(n-44) +309921*a(n-45) -290298*a(n-46) -125601*a(n-47) +305292*a(n-48) +136259*a(n-49) -258603*a(n-50) +61327*a(n-51) +159050*a(n-52) -38560*a(n-53) -141448*a(n-54) +129709*a(n-55) +7719*a(n-56) -44123*a(n-57) -7193*a(n-58) +55990*a(n-59) -13845*a(n-60) -8760*a(n-61) +20576*a(n-62) -2742*a(n-63) -2230*a(n-64) -2120*a(n-65) -936*a(n-66) -3164*a(n-67) -680*a(n-68) -848*a(n-70) for n>85

A241057 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 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, 6, 6, 64, 163, 280, 1423, 4167, 13389, 46605, 146031, 518568, 1559943, 5448063, 18661041, 57879161, 201222626, 664132824, 2176050370, 7339658200, 24139869513, 80786317859, 267972379590, 888853920796, 2971967179489, 9838548423147

Offset: 1

R. H. Hardin, Apr 15 2014

nonn

Row 4 of A241054

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

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

A241058 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 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, 8, 6, 132, 598, 1392, 10921, 72769, 370453, 1671155, 9384164, 51783699, 208252518, 1150802650, 6121081737, 27887287923, 140605229939, 756558481056, 3755762723973, 18153596088044, 90862001756655, 469665600883273

Offset: 1

R. H. Hardin, Apr 15 2014

nonn

Row 5 of A241054

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

R. H. Hardin, Table of n, a(n) for n = 1..31

cp's OEIS Frontend

A241050 Number of n X 2 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 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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A241051 Number of nX3 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 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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A241052 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 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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A241053 Number of n X 5 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 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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A241055 Number of 2 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 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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A241056 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 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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A241057 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 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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A241058 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 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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