A240792 -id:A240792 - cp's OEIS frontend

A240789 Number of n X 2 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 zero 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, 4, 5, 10, 13, 14, 30, 32, 36, 67, 79, 97, 173, 191, 232, 402, 464, 580, 960, 1104, 1400, 2250, 2637, 3388, 5280, 6255, 8117, 12342, 14819, 19374, 28826, 35008, 46021, 67233, 82554, 108956, 156715, 194316, 257170, 365065, 456688, 605532, 850096, 1071831

Offset: 1

R. H. Hardin, Apr 12 2014

nonn

			All solutions for n=4:
..3..3....3..3....3..3....3..3....3..2....3..2....3..3....3..2....3..3....3..3
..2..1....2..2....2..1....2..2....3..1....3..1....2..2....3..1....2..2....2..2
..3..3....3..1....3..3....3..1....2..2....2..1....3..3....2..2....3..1....3..1
..2..2....2..2....2..1....3..2....3..1....3..3....2..2....3..3....3..1....2..1

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

Column 2 of A240792.

Empirical: a(n) = 4*a(n-3) + a(n-5) - 3*a(n-6) - 3*a(n-8) - 4*a(n-9) + a(n-11) + 4*a(n-12) + 3*a(n-14) - 2*a(n-17) for n>19.

Empirical g.f.: x*(3 + 4*x + 5*x^2 - 2*x^3 - 3*x^4 - 9*x^5 - 5*x^6 - 13*x^7 - 6*x^8 - 12*x^9 + 7*x^10 + 12*x^11 + 26*x^12 + 8*x^13 - 8*x^14 - 17*x^15 - 5*x^16 + 5*x^17 + 2*x^18) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(1 - x^2 - x^3)*(1 - 2*x^3)*(1 + x^2 - x^3 + x^4 - x^5)). - Colin Barker, Oct 29 2018

A240790 Number of n X 3 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 zero 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, 5, 8, 27, 49, 50, 89, 115, 182, 289, 425, 651, 992, 1486, 2255, 3349, 5040, 7706, 11754, 17525, 26365, 39661, 59893, 89903, 135336, 203491, 306233, 460867, 692971, 1040765, 1565790, 2353754, 3540545, 5319995, 8000324, 12027862, 18084789

Offset: 1

R. H. Hardin, Apr 12 2014

nonn

Column 3 of A240792.

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

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

Cf. A240792.

Empirical: a(n) = 5*a(n-5) +4*a(n-6) +a(n-7) +4*a(n-8) +5*a(n-9) -6*a(n-10) -12*a(n-11) -a(n-12) -13*a(n-13) -16*a(n-14) -7*a(n-15) +13*a(n-16) +2*a(n-17) +20*a(n-18) +24*a(n-19) +15*a(n-20) -3*a(n-21) -2*a(n-22) -20*a(n-23) -44*a(n-24) -11*a(n-25) +9*a(n-26) -82*a(n-27) -30*a(n-28) +19*a(n-29) -21*a(n-30) -108*a(n-31) +132*a(n-32) +43*a(n-33) -68*a(n-34) +17*a(n-35) +171*a(n-36) -171*a(n-37) +66*a(n-38) +206*a(n-39) -46*a(n-40) -124*a(n-41) +214*a(n-42) -29*a(n-43) -283*a(n-44) +123*a(n-45) +129*a(n-46) -251*a(n-47) -6*a(n-48) +164*a(n-49) -17*a(n-50) -121*a(n-51) +216*a(n-52) +51*a(n-53) -79*a(n-54) +40*a(n-55) +58*a(n-56) -21*a(n-57) -16*a(n-58) +32*a(n-59) -3*a(n-60) -47*a(n-61) -29*a(n-62) -9*a(n-63) -2*a(n-64) -11*a(n-65) -2*a(n-66) +10*a(n-67) -6*a(n-69) +12*a(n-70) +3*a(n-71) -4*a(n-72) -3*a(n-73) +3*a(n-74) +a(n-75) -3*a(n-76) for n>87.

A240791 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 zero 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, 10, 19, 37, 85, 142, 386, 979, 1988, 5128, 10616, 25230, 58238, 125528, 302384, 670325, 1520808, 3524961, 7865967, 18151793, 41320633, 93575521, 215154289, 487353355, 1112746546, 2542170679, 5772347607, 13196888198, 30049864101

Offset: 1

R. H. Hardin, Apr 12 2014

nonn

Column 4 of A240792

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

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

A240793 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 zero 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, 4, 5, 10, 14, 24, 53, 70, 140, 237, 396, 730, 1242, 2166, 3743, 6547, 11397, 19760, 34622, 59868, 104358, 181794, 315863, 550264, 957027, 1665335, 2897587, 5042553, 8774919, 15266419, 26569228, 46226952, 80439383, 139977422, 243558497

Offset: 1

R. H. Hardin, Apr 12 2014

nonn

Row 2 of A240792

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

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

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

A240794 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 zero 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, 5, 8, 19, 34, 82, 278, 669, 1969, 3553, 9374, 26252, 60465, 172383, 389427, 951837, 2531963, 6160868, 15935881, 39165416, 97133522, 245493084, 614301686, 1554508080, 3857975809, 9676587733, 24254427054, 60670014406, 152847249733

Offset: 1

R. H. Hardin, Apr 12 2014

nonn

Row 3 of A240792

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

R. H. Hardin, Table of n, a(n) for n = 1..188

A240795 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 zero 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, 10, 27, 37, 132, 552, 2277, 11588, 35799, 109054, 467005, 1826688, 8078985, 27489845, 92673526, 369573835, 1387676052, 5728088537, 20522163467, 72766642122, 281548168173, 1050333422732, 4157767214229, 15271536502557

Offset: 1

R. H. Hardin, Apr 12 2014

nonn

Row 4 of A240792

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

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

cp's OEIS Frontend

A240789 Number of n X 2 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 zero 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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A240790 Number of n X 3 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 zero 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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A240791 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 zero 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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A240793 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 zero 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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A240794 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 zero 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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A240795 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 zero 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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