A239030 -id:A239030 - cp's OEIS frontend

A239024 Number of n X 2 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

1, 3, 4, 11, 16, 43, 64, 171, 256, 683, 1024, 2731, 4096, 10923, 16384, 43691, 65536, 174763, 262144, 699051, 1048576, 2796203, 4194304, 11184811, 16777216, 44739243, 67108864, 178956971, 268435456, 715827883, 1073741824, 2863311531, 4294967296

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

			Some solutions for n=5:
..2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0
..1..0....2..0....2..0....2..0....1..2....1..0....1..0....2..0....2..0....1..0
..2..0....1..2....1..0....1..2....2..1....2..0....2..0....1..2....1..2....2..0
..2..0....2..1....1..0....1..2....1..0....1..0....1..2....2..1....1..2....2..0
..1..2....1..2....2..0....2..1....2..0....2..0....2..1....1..0....2..0....1..0

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

Column 2 of A239030.

Empirical: a(n) = 5*a(n-2) - 4*a(n-4).
Conjectures from Colin Barker, Oct 25 2018: (Start)
G.f.: x*(1 + 3*x - x^2 - 4*x^3) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)).
a(n) = (2 + (-2)^n + 2*(-1)^n + 7*2^n) / 12.
(End)

A239025 Number of n X 3 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

Original entry on oeis.org

1, 4, 7, 28, 54, 212, 428, 1652, 3410, 13004, 27158, 102740, 215998, 812892, 1715842, 6435860, 13618366, 50970780, 108022954, 403751540, 856522206, 3198552316, 6789722794, 25340854612, 53813984430, 200773770908, 426474521338

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

			Some solutions for n=5:
..2..0..0....2..0..0....2..0..0....2..0..0....2..0..0....2..0..0....2..0..0
..1..0..0....1..0..2....1..0..0....1..2..2....1..0..0....2..0..0....2..0..0
..2..0..0....2..0..1....2..0..0....2..1..1....2..0..0....1..0..2....1..0..0
..1..2..2....1..2..2....1..2..2....2..0..0....2..0..0....2..0..1....2..0..0
..2..1..1....2..1..2....2..1..2....1..0..2....1..2..2....1..0..0....1..0..2

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

Column 3 of A239030.

Empirical: a(n) = 17*a(n-2) - 96*a(n-4) + 210*a(n-6) - 152*a(n-8).

Empirical g.f.: x*(1 + 4*x - 10*x^2 - 40*x^3 + 31*x^4 + 120*x^5 - 28*x^6 - 104*x^7) / (1 - 17*x^2 + 96*x^4 - 210*x^6 + 152*x^8). - Colin Barker, Oct 25 2018

A239026 Number of nX4 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

Original entry on oeis.org

1, 5, 11, 59, 149, 806, 2195, 11768, 33417, 177087, 514763, 2701462, 7959113, 41470771, 123166255, 638542081, 1905821801, 9846665639, 29480427979, 151961034078, 455874537477, 2346202859972, 7047642531511, 36233420401775

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

Column 4 of A239030

			Some solutions for n=5
..2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0
..1..0..0..2....2..0..0..0....1..0..2..2....1..0..2..2....2..0..0..0
..2..0..0..1....1..0..0..0....2..0..1..2....2..0..1..2....1..2..2..0
..1..0..0..0....1..2..2..0....2..0..0..1....1..2..2..0....2..1..1..2
..2..0..0..0....2..1..1..0....1..2..2..1....2..1..2..0....1..0..0..2

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

Empirical: a(n) = 50*a(n-2) -1020*a(n-4) +11131*a(n-6) -71319*a(n-8) +275531*a(n-10) -629492*a(n-12) +789744*a(n-14) -456320*a(n-16) +76800*a(n-18)

A239027 Number of nX5 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

Original entry on oeis.org

1, 6, 16, 110, 354, 2592, 9319, 69288, 265247, 1965398, 7800825, 57331200, 232485057, 1695069696, 6964531270, 50452937884, 209015936546, 1506842267076, 6275879711407, 45084885342398, 188433761914537, 1350270184320046

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

Column 5 of A239030

			Some solutions for n=5
..2..0..0..0..0....2..0..0..0..0....2..0..0..0..0....2..0..0..0..0
..1..0..0..2..2....1..0..0..2..2....1..2..2..0..0....1..0..2..2..0
..2..0..0..1..1....2..0..0..1..2....2..1..1..0..2....2..0..1..2..0
..2..0..0..0..0....1..2..2..0..0....2..0..0..0..1....2..0..0..1..2
..1..0..0..2..2....2..1..2..0..0....1..0..0..0..2....1..2..2..1..2

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

Empirical: a(n) = 167*a(n-2) -12737*a(n-4) +590522*a(n-6) -18674960*a(n-8) +428232709*a(n-10) -7384832953*a(n-12) +97981999331*a(n-14) -1014383126841*a(n-16) +8257937387592*a(n-18) -53002256526176*a(n-20) +267655608403835*a(n-22) -1056157718233604*a(n-24) +3216196113264380*a(n-26) -7411332048725488*a(n-28) +12543993016224416*a(n-30) -14892794784221696*a(n-32) +11503438838397440*a(n-34) -5030303892805632*a(n-36) +890642713919488*a(n-38)

A239028 Number of nX6 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

Original entry on oeis.org

1, 7, 22, 189, 757, 7265, 33699, 339315, 1719471, 17562449, 93885393, 958423704, 5294453737, 53749275243, 303098123295, 3057605672892, 17472132232105, 175268385351709, 1010298392497549, 10088889232010085, 58495304591252863

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

Column 6 of A239030

			Some solutions for n=5
..2..0..0..0..0..0....2..0..0..0..0..0....2..0..0..0..0..0....2..0..0..0..0..0
..1..0..0..2..2..0....1..0..0..2..2..0....1..0..0..0..0..0....1..2..2..0..0..0
..2..0..0..1..1..2....2..0..0..1..2..0....2..0..0..0..0..0....2..1..1..2..2..0
..2..0..0..0..0..1....1..2..2..0..0..0....1..2..2..0..0..0....2..0..0..1..2..0
..1..0..0..2..2..0....2..1..2..0..0..0....2..1..1..0..0..2....1..0..0..0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 90

Empirical recurrence of order 90 (see link above)

A239029 Number of nX7 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

Original entry on oeis.org

1, 8, 29, 306, 1495, 18362, 107611, 1435014, 9453266, 131139508, 930867565, 13097850256, 97472804219, 1373719026116, 10536457574723, 147977950815572, 1157525035823201, 16176954064274638, 128205153484308223

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

Column 7 of A239030

			Some solutions for n=5
..2..0..0..0..0..0..0....2..0..0..0..0..0..0....2..0..0..0..0..0..0
..2..0..0..0..0..0..0....1..2..2..0..0..0..0....1..2..2..0..0..0..0
..1..0..2..2..0..0..0....2..1..1..0..2..2..0....2..1..2..0..0..0..0
..2..0..1..1..0..2..2....1..0..2..2..1..1..2....2..0..0..0..0..0..0
..1..0..0..2..2..1..1....2..0..1..1..0..0..2....1..0..0..0..0..0..0

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

A239031 Number of 4 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

Original entry on oeis.org

4, 11, 28, 59, 110, 189, 306, 473, 704, 1015, 1424, 1951, 2618, 3449, 4470, 5709, 7196, 8963, 11044, 13475, 16294, 19541, 23258, 27489, 32280, 37679, 43736, 50503, 58034, 66385, 75614, 85781, 96948, 109179, 122540, 137099, 152926, 170093, 188674

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

			Some solutions for n=5:
..2..0..0..0..0....2..0..0..0..0....2..0..0..0..0....2..0..0..0..0
..2..0..0..0..0....1..0..2..2..0....1..0..0..0..2....2..0..0..0..0
..1..0..0..0..0....2..0..1..1..2....2..0..0..0..1....1..0..2..2..0
..1..0..0..0..2....1..2..2..0..1....1..0..0..0..2....2..0..1..2..0

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

Row 4 of A239030.

Empirical: a(n) = (1/12)*n^4 - (1/6)*n^3 + (47/12)*n^2 - (29/6)*n + 5.
Conjectures from Colin Barker, Oct 25 2018: (Start)
G.f.: x*(4 - 9*x + 13*x^2 - 11*x^3 + 5*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A239032 Number of 5 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

Original entry on oeis.org

4, 16, 54, 149, 354, 757, 1495, 2773, 4888, 8258, 13456, 21249, 32642, 48927, 71737, 103105, 145528, 202036, 276266, 372541, 495954, 652457, 848955, 1093405, 1394920, 1763878, 2212036, 2752649, 3400594, 4172499, 5086877, 6164265, 7427368, 8901208

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

			Some solutions for n=5:
..2..0..0..0..0....2..0..0..0..0....2..0..0..0..0....2..0..0..0..0
..2..0..0..0..0....2..0..0..0..0....1..0..2..2..0....2..0..0..0..0
..1..0..2..2..0....1..0..0..2..2....2..0..1..1..0....1..0..0..0..2
..2..0..1..1..0....1..2..2..1..2....2..0..0..0..0....1..2..2..0..1
..1..0..0..0..0....2..1..1..0..0....1..2..2..0..0....2..1..1..0..2

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

Row 5 of A239030.

Empirical: a(n) = (1/144)*n^6 - (17/240)*n^5 + (169/144)*n^4 - (81/16)*n^3 + (1463/72)*n^2 - (1001/30)*n + 25 for n>1.
Conjectures from Colin Barker, Oct 25 2018: (Start)
G.f.: x*(4 - 12*x + 26*x^2 - 33*x^3 + 25*x^4 - 6*x^5 - 3*x^6 + 4*x^7) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>8.
(End)

A239033 Number of 6 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

Original entry on oeis.org

8, 43, 212, 806, 2592, 7265, 18362, 42809, 93464, 193157, 380900, 721154, 1317296, 2330727, 4007402, 6713945, 10985936, 17591423, 27613220, 42554102, 64469600, 96133733, 141243690, 204670193, 292761032, 413706065, 577972820, 798822722

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

			Some solutions for n=5:
..2..0..0..0..0....2..0..0..0..0....2..0..0..0..0....2..0..0..0..0
..2..0..0..0..0....1..0..0..2..2....2..0..0..0..0....2..0..0..0..0
..1..2..2..0..0....2..0..0..1..2....1..0..0..0..0....1..0..0..0..2
..2..1..1..2..2....2..0..0..0..0....2..0..0..0..0....1..2..2..0..1
..1..2..2..1..2....1..0..2..2..0....1..0..0..2..2....2..1..1..2..2
..1..2..1..0..0....1..2..1..2..1....1..0..0..2..1....1..0..2..1..2

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

Row 6 of A239030.

Empirical: a(n) = (1/8640)*n^9 - (61/20160)*n^8 + (263/3360)*n^7 - (1439/1440)*n^6 + (29843/2880)*n^5 - (194227/2880)*n^4 + (668597/2160)*n^3 - (1477657/1680)*n^2 + (59263/42)*n - 943 for n>2.
Conjectures from Colin Barker, Oct 25 2018: (Start)
G.f.: x*(8 - 37*x + 142*x^2 - 339*x^3 + 592*x^4 - 811*x^5 + 996*x^6 - 1020*x^7 + 792*x^8 - 377*x^9 + 88*x^10 + 8*x^11) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>12.
(End)

A239034 Number of 7Xn 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

Original entry on oeis.org

8, 64, 428, 2195, 9319, 33699, 107611, 311585, 833304, 2086074, 4936712, 11126665, 24022753, 49913047, 100179401, 194844297, 368222528, 677728244, 1217319704, 2137637135, 3675638019, 6197499195, 10259782783, 16695406105, 26732874536

Offset: 1

R. H. Hardin, Mar 09 2014

nonn

Row 7 of A239030

			Some solutions for n=5
..2..0..0..0..0....2..0..0..0..0....2..0..0..0..0....2..0..0..0..0
..2..0..0..0..0....1..2..2..0..0....1..2..2..0..0....2..0..0..0..0
..1..0..0..2..2....2..1..1..2..2....2..1..1..2..2....1..2..2..0..0
..2..0..0..1..2....1..0..0..2..2....1..2..2..1..2....2..1..1..2..2
..1..0..2..2..0....2..0..0..1..1....2..1..1..0..0....1..2..2..1..1
..1..0..2..1..0....2..0..0..1..1....2..0..0..0..0....1..2..2..0..0
..2..0..1..2..0....1..0..0..0..0....1..2..2..0..1....2..0..1..2..0

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

Empirical: a(n) = (1/1036800)*n^12 - (1961/39916800)*n^11 + (13339/7257600)*n^10 - (30521/725760)*n^9 + (583409/806400)*n^8 - (400873/44800)*n^7 + (86137751/1036800)*n^6 - (407381983/725760)*n^5 + (4957467353/1814400)*n^4 - (8367100109/907200)*n^3 + (515324983/25200)*n^2 - (185067023/6930)*n + 15601 for n>3

cp's OEIS Frontend

A239024 Number of n X 2 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

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A239025 Number of n X 3 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

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A239026 Number of nX4 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

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A239027 Number of nX5 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

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A239028 Number of nX6 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

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A239029 Number of nX7 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.

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A239031 Number of 4 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

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A239032 Number of 5 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

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A239033 Number of 6 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

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A239034 Number of 7Xn 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

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