A240039 -id:A240039 - cp's OEIS frontend

A240034 Number of n X 3 0..2 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, modulo 3.

4, 6, 16, 16, 42, 44, 114, 122, 314, 340, 872, 950, 2432, 2658, 6798, 7442, 19024, 20844, 53270, 58392, 149210, 163594, 418006, 458356, 1171124, 1284250, 3281268, 3598338, 9193694, 10082246, 25759848, 28249720, 72177042, 79153804, 202234930

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

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

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

Column 3 of A240039.

Empirical: a(n) = 4*a(n-2) - 3*a(n-4) -a(n-6) for n>7.

Empirical g.f.: 2*x*(2 + 3*x - 4*x^3 - 5*x^4 - x^5 - x^6) / (1 - 4*x^2 + 3*x^4 + x^6). - Colin Barker, Oct 27 2018

A240035 Number of nX4 0..2 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, modulo 3.

Original entry on oeis.org

4, 4, 16, 18, 52, 62, 162, 204, 530, 672, 1736, 2198, 5706, 7202, 18780, 23604, 61718, 77292, 202468, 252872, 663072, 826512, 2168300, 2698978, 7082068, 8806712, 23110072, 28718278, 75360086, 93603560, 245616936, 304976256, 800224510

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Column 4 of A240039

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

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

Empirical: a(n) = 11*a(n-2) -49*a(n-4) +117*a(n-6) -177*a(n-8) +214*a(n-10) -239*a(n-12) +207*a(n-14) -135*a(n-16) +108*a(n-18) -82*a(n-20) +29*a(n-22) -3*a(n-24) for n>27

A240036 Number of nX5 0..2 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, modulo 3.

Original entry on oeis.org

8, 10, 42, 52, 154, 178, 494, 600, 1606, 2014, 5262, 6690, 17464, 22360, 58342, 74736, 194784, 249738, 650892, 834326, 2174114, 2786028, 7260062, 9299282, 24230362, 31026484, 80832010, 103476740, 269526292, 344976344, 898349934, 1149695244

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Column 5 of A240039

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

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

Empirical: a(n) = 24*a(n-2) -254*a(n-4) +1540*a(n-6) -5743*a(n-8) +12572*a(n-10) -9844*a(n-12) -29846*a(n-14) +118468*a(n-16) -204106*a(n-18) +182686*a(n-20) +18168*a(n-22) -371269*a(n-24) +732749*a(n-26) -915915*a(n-28) +882644*a(n-30) -769800*a(n-32) +661777*a(n-34) -565432*a(n-36) +534609*a(n-38) -520131*a(n-40) +330402*a(n-42) -7073*a(n-44) -202359*a(n-46) +322607*a(n-48) -341400*a(n-50) +75883*a(n-52) +180888*a(n-54) -214325*a(n-56) +211488*a(n-58) -133525*a(n-60) +39168*a(n-62) -41213*a(n-64) +32114*a(n-66) +51*a(n-68) -15949*a(n-70) +5028*a(n-72) +5318*a(n-74) +1581*a(n-76) -642*a(n-78) +392*a(n-80) -233*a(n-82) -14*a(n-84) +4*a(n-86) for n>89

A240037 Number of nX6 0..2 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, modulo 3.

Original entry on oeis.org

8, 8, 44, 62, 178, 282, 710, 1074, 2770, 4162, 10836, 15764, 41374, 59680, 156886, 225150, 588814, 847438, 2209382, 3180402, 8266052, 11933946, 30940004, 44734494, 115726028, 167666138, 433004540, 628085454, 1619697032, 2352404846

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Column 6 of A240039

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

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

A240038 Number of nX7 0..2 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, modulo 3.

Original entry on oeis.org

16, 20, 114, 162, 494, 710, 1976, 2884, 7958, 12074, 31824, 49078, 130758, 197208, 535668, 803976, 2179014, 3283200, 8870448, 13320072, 36010660, 54089046, 145864864, 219566360, 590450318, 889464830, 2389662890, 3599725594

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Column 7 of A240039

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

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

A240033 Number of n X n 0..2 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, modulo 3.

Original entry on oeis.org

2, 2, 16, 18, 154, 282, 1976, 5706, 42470, 147092, 1196210, 5215010, 48697758, 245354078, 2815029508, 16378986516

Offset: 1

R. H. Hardin, Mar 31 2014

nonn

Diagonal of A240039

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

cp's OEIS Frontend

A240034 Number of n X 3 0..2 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, modulo 3.

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A240035 Number of nX4 0..2 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, modulo 3.

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A240036 Number of nX5 0..2 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, modulo 3.

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A240037 Number of nX6 0..2 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, modulo 3.

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A240038 Number of nX7 0..2 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, modulo 3.

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A240033 Number of n X n 0..2 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, modulo 3.

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