A263714 -id:A263714 - cp's OEIS frontend

A263710 Number of length n arrays of permutations of 0..n-1 with each element moved by -1 to 1 places and every four consecutive elements having its maximum within 4 of its minimum.

1, 2, 3, 5, 8, 11, 17, 25, 37, 57, 84, 127, 191, 284, 429, 641, 961, 1445, 2161, 3246, 4867, 7293, 10948, 16407, 24609, 36913, 55337, 83009, 124472, 186655, 279951, 419784, 629561, 944129, 1415809, 2123305, 3184145, 4775114, 7161091, 10738981, 16104880

Offset: 1

R. H. Hardin, Oct 24 2015

nonn

			Some solutions for n=7:
..0....0....0....0....1....0....0....1....1....0....1....1....0....0....1....0
..2....1....2....2....0....1....1....0....0....1....0....0....1....1....0....1
..1....2....1....1....2....2....2....2....2....3....2....3....2....3....3....3
..3....3....3....4....3....3....4....4....4....2....3....2....4....2....2....2
..4....4....5....3....4....4....3....3....3....4....4....4....3....4....4....5
..5....6....4....5....6....5....5....6....5....5....5....6....6....6....5....4
..6....5....6....6....5....6....6....5....6....6....6....5....5....5....6....6

R. H. Hardin, Table of n, a(n) for n = 1..210
Michael A. Allen, Combinations without specified separations and restricted-overlap tiling with combs, arXiv:2210.08167 [math.CO], 2022.

Column 1 of A263714.

Empirical: a(n) = a(n-1) + a(n-3) - a(n-4) + 2*a(n-5) - a(n-6) + a(n-7).

Empirical g.f.: x*(1 - x + x^2)*(1 + 2*x + 2*x^2 + x^3 + x^4) / (1 - x - x^3 + x^4 - 2*x^5 + x^6 - x^7). - Colin Barker, Jan 02 2019

A263711 Number of length n arrays of permutations of 0..n-1 with each element moved by -2 to 2 places and every four consecutive elements having its maximum within 4 of its minimum.

Original entry on oeis.org

1, 2, 6, 14, 31, 34, 39, 46, 64, 104, 161, 249, 385, 561, 845, 1254, 1871, 2833, 4228, 6359, 9545, 14273, 21453, 32133, 48184, 72323, 108363, 162592, 243817, 365545, 548369, 822181, 1233053, 1849282, 2772959, 4158841, 6236608, 9352579, 14026153

Offset: 1

R. H. Hardin, Oct 24 2015

nonn

			Some solutions for n=7:
..1....0....1....1....0....0....0....1....0....1....0....0....2....1....1....0
..0....1....0....0....1....1....1....0....2....0....1....1....0....0....0....1
..4....2....2....3....4....3....3....3....1....3....4....2....1....2....4....2
..2....3....3....4....3....4....4....2....3....4....2....4....4....3....3....4
..3....5....4....2....2....2....2....4....4....2....5....3....3....4....2....5
..6....4....5....6....6....6....5....5....5....5....3....5....5....6....5....3
..5....6....6....5....5....5....6....6....6....6....6....6....6....5....6....6

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

Column 2 of A263714.

Empirical: a(n) = a(n-1) + a(n-3) - a(n-4) + 2*a(n-5) - a(n-6) + a(n-7) for n>18.

Empirical g.f.: x*(1 + x + 4*x^2 + 7*x^3 + 16*x^4 - 3*x^5 - 6*x^6 - 21*x^7 - 9*x^8 - 19*x^9 - x^10 - 5*x^11 + 9*x^12 - 2*x^13 + 6*x^14 - 9*x^15 - 4*x^17) / (1 - x - x^3 + x^4 - 2*x^5 + x^6 - x^7). - Colin Barker, Jan 02 2019

A263712 Number of length n arrays of permutations of 0..n-1 with each element moved by -3 to 3 places and every four consecutive elements having its maximum within 4 of its minimum.

Original entry on oeis.org

1, 2, 6, 24, 78, 60, 50, 52, 70, 116, 184, 292, 449, 649, 969, 1429, 2137, 3238, 4839, 7285, 10924, 16339, 24553, 36769, 55153, 82769, 124024, 186099, 279039, 418384, 627613, 940985, 1411273, 2116505, 3173705, 4759874, 7137847, 10704221, 16053112

Offset: 1

R. H. Hardin, Oct 24 2015

nonn

			Some solutions for n=7:
..0....0....1....3....1....0....0....0....0....1....0....0....0....0....0....1
..1....3....0....0....0....1....4....1....4....0....1....4....1....1....1....0
..3....1....2....1....4....3....1....2....1....2....4....1....4....2....4....3
..4....4....4....4....2....4....2....3....3....3....2....2....2....4....2....4
..2....2....3....2....3....2....3....5....5....4....5....5....3....3....3....2
..6....5....6....5....6....5....5....6....2....6....6....3....5....5....6....5
..5....6....5....6....5....6....6....4....6....5....3....6....6....6....5....6

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

Column 3 of A263714.

Empirical: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18.

Empirical g.f.: x*(1 + x + 4*x^2 + 17*x^3 + 53*x^4 - 24*x^5 - 31*x^6 - 63*x^7 - 8*x^8 - 82*x^9 - 28*x^11 - 3*x^12 - 6*x^13 - 2*x^14 - 19*x^15 - 8*x^16 - 9*x^17) / (1 - x - x^3 + x^4 - 2*x^5 + x^6 - x^7). - Colin Barker, Jan 02 2019

A263713 Number of length n arrays of permutations of 0..n-1 with each element moved by -4 to 4 places and every four consecutive elements having its maximum within 4 of its minimum.

Original entry on oeis.org

1, 2, 6, 24, 120, 72, 54, 54, 72, 120, 192, 308, 480, 688, 1024, 1504, 2244, 3408, 5092, 7672, 11508, 17200, 25856, 38712, 58064, 87156, 130576, 195948, 293808, 440500, 660832, 990752, 1485920, 2228496, 3341556, 5011696, 7515444, 11270424, 16902388

Offset: 1

R. H. Hardin, Oct 24 2015

nonn

			Some solutions for n=7:
..0....0....0....0....0....1....0....0....1....4....0....0....0....0....0....0
..4....2....3....1....1....0....1....1....0....0....1....4....1....3....1....1
..1....1....1....2....2....3....4....3....2....1....4....1....3....1....3....2
..2....3....2....4....4....2....2....2....3....3....2....2....4....4....2....3
..3....5....4....5....3....4....5....5....4....2....3....5....2....2....4....4
..5....4....5....6....6....5....3....6....5....5....5....3....5....5....6....5
..6....6....6....3....5....6....6....4....6....6....6....6....6....6....5....6

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

Column 4 of A263714.

Empirical: a(n) = a(n-1) +a(n-3) -a(n-4) +2*a(n-5) -a(n-6) +a(n-7) for n>18.

Empirical g.f.: x*(1 + x + 4*x^2 + 17*x^3 + 95*x^4 - 54*x^5 - 39*x^6 - 107*x^7 + 22*x^8 - 156*x^9 + 24*x^10 - 58*x^11 - 2*x^12 - 8*x^13 - 2*x^14 - 28*x^15 - 12*x^16 - 16*x^17) / (1 - x - x^3 + x^4 - 2*x^5 + x^6 - x^7). - Colin Barker, Jan 02 2019

A263709 Number of length n arrays of permutations of 0..n-1 with each element moved by -n to n places and every four consecutive elements having its maximum within 4 of its minimum.

Original entry on oeis.org

1, 2, 6, 24, 120, 144, 108, 108, 144, 240, 384, 616, 960, 1376, 2048, 3008, 4488, 6816, 10184, 15344, 23016

Offset: 1

R. H. Hardin, Oct 24 2015

nonn

Diagonal of A263714

			Some solutions for n=7
..1....5....0....1....6....0....3....6....0....3....0....6....0....0....0....0
..0....6....4....0....2....2....0....5....1....6....3....5....1....1....1....1
..2....4....1....3....5....1....1....4....3....5....1....2....3....3....2....4
..3....2....2....2....3....3....4....3....2....4....4....3....4....2....4....2
..4....3....3....4....1....5....2....2....5....2....5....1....5....4....3....5
..6....1....5....6....4....4....5....1....4....1....2....4....6....6....6....3
..5....0....6....5....0....6....6....0....6....0....6....0....2....5....5....6

Cf. A263714

cp's OEIS Frontend

A263710 Number of length n arrays of permutations of 0..n-1 with each element moved by -1 to 1 places and every four consecutive elements having its maximum within 4 of its minimum.

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A263711 Number of length n arrays of permutations of 0..n-1 with each element moved by -2 to 2 places and every four consecutive elements having its maximum within 4 of its minimum.

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A263712 Number of length n arrays of permutations of 0..n-1 with each element moved by -3 to 3 places and every four consecutive elements having its maximum within 4 of its minimum.

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A263713 Number of length n arrays of permutations of 0..n-1 with each element moved by -4 to 4 places and every four consecutive elements having its maximum within 4 of its minimum.

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A263709 Number of length n arrays of permutations of 0..n-1 with each element moved by -n to n places and every four consecutive elements having its maximum within 4 of its minimum.

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