A241397 -id:A241397 - cp's OEIS frontend

A241392 Number of nX2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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, 5, 13, 28, 64, 142, 318, 726, 1634, 3695, 8363, 18904, 42787, 96771, 218940, 495514, 1121224, 2537388, 5742666, 12996786, 29415660, 66576728, 150686121, 341060866, 771951453, 1747237409, 3954724092, 8951198975, 20260385570, 45857968649

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Column 2 of A241397

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

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)

A241393 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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, 29, 97, 340, 1156, 4068, 14763, 52950, 190950, 687442, 2476661, 8922447, 32121858, 115744464, 416837976, 1501406960, 5406257970, 19472791326, 70130249296, 252570497669, 909559808019, 3275792914936, 11797588596607

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Column 3 of A241397

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

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

A241394 Number of n X 4 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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, 23, 85, 480, 2780, 17211, 102782, 645484, 3936420, 24633252, 150911826, 941907715, 5783836527, 36025719987, 221566632164, 1377925800191, 8486654284672, 52714390850462, 324976079474744, 2016735929148039, 12443708121368662, 77167572875652387, 476406669588897579

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

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

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

Column 4 of A241397.

A241398 Number of 2Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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

3, 5, 9, 23, 44, 93, 204, 368, 761, 1583, 2951, 6056, 12244, 23588, 47945, 95715, 187731, 378531, 752679, 1489014, 2986657, 5934705, 11787915, 23567455, 46847503, 93218990, 186017656, 369978815, 736728537, 1468604461, 2922396725, 5820645191

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Row 2 of A241397

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

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

Empirical: a(n) = 2*a(n-2) +8*a(n-3) -a(n-4) -10*a(n-5) -18*a(n-6) +8*a(n-7) +20*a(n-8) +20*a(n-9) -24*a(n-10) -22*a(n-11) -a(n-12) +32*a(n-13) +8*a(n-14) -3*a(n-15) -12*a(n-16) +4*a(n-17) -5*a(n-18) -4*a(n-20) -3*a(n-21) +2*a(n-22) for n>23

A241399 Number of 3Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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, 13, 29, 85, 201, 689, 1929, 4068, 11963, 33651, 80035, 231111, 606571, 1542322, 4407947, 11308092, 29789742, 82990169, 213582987, 572318731, 1556503937, 4056412623, 10923983311, 29272912317, 77140259839, 207516834784

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Row 3 of A241397

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

R. H. Hardin, Table of n, a(n) for n = 1..143

A241400 Number of 4Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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

7, 28, 97, 480, 1657, 8697, 31654, 92204, 397955, 1440202, 5015494, 20114505, 70074714, 258768285, 999131434, 3471187281, 13084431710, 49495338616, 176036491899, 662243630484, 2450968267032, 8911921597230, 33375847400152

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Row 4 of A241397

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

R. H. Hardin, Table of n, a(n) for n = 1..136

A241395 Number of nX5 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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, 44, 201, 1657, 15339, 160947, 1622867, 18627122, 196990531, 2356216195, 25594964973, 309860295135, 3406115792732, 41329346536802, 457205784409075, 5541954581513250, 61567408955078580, 744650178324042533

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Column 5 of A241397

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

A241396 Number of nX6 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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, 93, 689, 8697, 129985, 2234804, 39781828, 821631365, 16108803423, 370391699130

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Column 6 of A241397

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

A241401 Number of 5Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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

10, 64, 340, 2780, 15339, 129985, 667050, 2949778, 18902401, 91648139, 516486984, 3075569596, 15073466440, 85957361897, 473425616837, 2340472941060, 13328226383734, 73626242006464, 386042800402280, 2155794635092538

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Row 5 of A241397

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

A241402 Number of 6Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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

15, 142, 1156, 17211, 160947, 2234804, 18589398, 134190457, 1305599583, 8782028493, 85981849830

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Row 6 of A241397

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

cp's OEIS Frontend

A241392 Number of nX2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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A241393 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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A241394 Number of n X 4 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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A241398 Number of 2Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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A241399 Number of 3Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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A241400 Number of 4Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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A241395 Number of nX5 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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A241396 Number of nX6 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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A241401 Number of 5Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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A241402 Number of 6Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one 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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