A239986 -id:A239986 - cp's OEIS frontend

A239980 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

1, 3, 6, 16, 40, 84, 208, 474, 1047, 2530, 5668, 12907, 30446, 68427, 157875, 366480, 830089, 1920870, 4421253, 10083067, 23303103, 53453752, 122448587, 282350403, 647215090, 1486007814, 3420002865, 7842656682, 18022838258, 41428828907

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

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

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

Column 2 of A239986.

Empirical: a(n) = 2*a(n-2) + 10*a(n-3) - a(n-4) - 5*a(n-5) - 15*a(n-6) + a(n-7) + 4*a(n-8) + 2*a(n-9) + 10*a(n-10) + 5*a(n-11) - 6*a(n-13).

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

A239981 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

1, 4, 13, 56, 261, 935, 4113, 16724, 63746, 275188, 1085962, 4300307, 18095718, 71121297, 287888587, 1186770242, 4693927215, 19155022357, 77909148678, 310802944863, 1269055778212, 5125935099711, 20593563815344, 83875501530044

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Column 3 of A239986

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

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

A239982 Number of nX4 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

1, 5, 22, 171, 1391, 9079, 70107, 514297, 3533132, 27478686, 195617485, 1396299371, 10574699363, 74869696354, 547239827048, 4060652644276, 28932235350938, 213204213265435, 1560042805514282, 11221251973358733, 82689323867874597

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Column 4 of A239986

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

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

A239983 Number of nX5 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

1, 6, 38, 530, 7113, 83658, 1174822, 15307425, 192702130, 2733573580, 34877309132, 455831231370, 6232060203371, 79504957220188, 1061047782962716, 14175980247721974, 182879377335377352, 2451126765466429888

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Column 5 of A239986

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

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

A239984 Number of nX6 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

1, 7, 65, 1495, 31226, 652346, 16721012, 381369904, 9009351655, 233083355837, 5373732732783, 130821770741989, 3240495708022575, 75383547521530003, 1859081645190913254, 44959584675029390497, 1062939483571455261657

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Column 6 of A239986

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

R. H. Hardin, Table of n, a(n) for n = 1..19

A239987 Number of 3 X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

3, 6, 13, 22, 38, 65, 107, 169, 257, 378, 540, 752, 1024, 1367, 1793, 2315, 2947, 3704, 4602, 5658, 6890, 8317, 9959, 11837, 13973, 16390, 19112, 22164, 25572, 29363, 33565, 38207, 43319, 48932, 55078, 61790, 69102, 77049, 85667, 94993, 105065

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

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

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

Row 3 of A239986.

Empirical: a(n) = (1/24)*n^4 - (1/4)*n^3 + (71/24)*n^2 - (43/4)*n + 23 for n>3.
Conjectures from Colin Barker, Oct 27 2018: (Start)
G.f.: x*(3 - 9*x + 13*x^2 - 13*x^3 + 13*x^4 - 8*x^5 + x^6 + x^7) / (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>8.
(End)

A239988 Number of 4Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

4, 16, 56, 171, 530, 1495, 4059, 10121, 23476, 51169, 105957, 210063, 401043, 740392, 1325954, 2309449, 3920715, 6500605, 10544919, 16762214, 26148867, 40085363, 60458446, 89814510, 131550423, 190148874, 271466315, 383082641, 534722915

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Row 4 of A239986

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

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

Empirical: a(n) = (1/907200)*n^10 - (1/72576)*n^9 + (113/120960)*n^8 - (265/12096)*n^7 + (2651/5400)*n^6 - (141761/17280)*n^5 + (40878671/362880)*n^4 - (10305217/9072)*n^3 + (399085217/50400)*n^2 - (86061371/2520)*n + 68243 for n>12

A239989 Number of 5Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

7, 40, 261, 1391, 7113, 31226, 131242, 514539, 1914507, 6772946, 22897312, 74168162, 230889987, 691544987, 1994352403, 5541664374, 14851119427, 38433580993, 96194422578, 233234971795, 548761214881, 1255035407604

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Row 5 of A239986

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 24

Empirical polynomial of degree 24 (see link above)

A239990 Number of 6Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

10, 84, 935, 9079, 83658, 652346, 4803152, 33097266, 216706121, 1349071998, 8021288399, 45621294425, 248975151409, 1305176292249, 6573063784889, 31800829162681, 147862529519971, 661287427073134, 2848137371338660

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Row 6 of A239986

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 55

Empirical polynomial of degree 55 (see link above)

A239991 Number of 7 X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

15, 208, 4113, 70107, 1174822, 16721012, 226886115, 2823199343, 33074332722, 366468588411, 3862531765288, 38827887664460, 374132975836928, 3462018008021025, 30769710869286232, 262533007814160639

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Row 7 of A239986.

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

R. H. Hardin, Table of n, a(n) for n = 1..53

cp's OEIS Frontend

A239980 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239981 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239982 Number of nX4 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239983 Number of nX5 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239984 Number of nX6 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239987 Number of 3 X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239988 Number of 4Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239989 Number of 5Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239990 Number of 6Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239991 Number of 7 X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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