cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A263690 Number of length n arrays of permutations of 0..n-1 with each element moved by -n to n places and every three consecutive elements having its maximum within 3 of its minimum.

Original entry on oeis.org

1, 1, 2, 6, 24, 36, 36, 48, 80, 128, 200, 288, 432, 648, 992, 1496, 2272, 3424, 5192, 7840, 11880, 17952, 27184, 41096, 62208, 94072, 142368, 215328, 325832, 492864, 745736, 1128096, 1706800, 2582024, 3906464, 5909784, 8941024, 13526368, 20464072, 30959200
Offset: 0

Views

Author

R. H. Hardin, Oct 23 2015

Keywords

Links

Crossrefs

Diagonal of A263693.
Cf. A333833.

Formula

Empirical: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>12.
G.f.: (8*x^12+8*x^11-4*x^10-8*x^8+6*x^7+20*x^6-7*x^5-16*x^4-4*x^3-1) / (x^4-x^3+x^2+x-1). - Alois P. Heinz, Apr 08 2020

Extensions

a(0), a(24)-a(39) from Alois P. Heinz, Apr 08 2020

A263691 Number of length n arrays of permutations of 0..n-1 with each element moved by -2 to 2 places and every three consecutive elements having its maximum within 3 of its minimum.

Original entry on oeis.org

1, 2, 6, 14, 14, 16, 22, 36, 56, 85, 125, 189, 285, 434, 655, 993, 1499, 2271, 3432, 5197, 7857, 11893, 17985, 27218, 41167, 62293, 94227, 142571, 215672, 326309, 493637, 746845, 1129845, 1709362, 2585999, 3912361, 5918843, 8954567, 13547048
Offset: 1

Views

Author

R. H. Hardin, Oct 23 2015

Keywords

Examples

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

Links

Crossrefs

Column 2 of A263693.

Formula

Empirical: a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) for n>12.
Empirical g.f.: x*(1 + x + 3*x^2 + 7*x^3 - 5*x^4 - 8*x^5 - 2*x^7 - x^9 - 2*x^10 - x^11) / (1 - x - x^2 + x^3 - x^4). - Colin Barker, Jan 02 2019

A263692 Number of length n arrays of permutations of 0..n-1 with each element moved by -3 to 3 places and every three consecutive elements having its maximum within 3 of its minimum.

Original entry on oeis.org

1, 2, 6, 24, 18, 18, 24, 40, 64, 100, 144, 216, 324, 496, 748, 1136, 1712, 2596, 3920, 5940, 8976, 13592, 20548, 31104, 47036, 71184, 107664, 162916, 246432, 372868, 564048, 853400, 1291012, 1953232, 2954892, 4470512, 6763184, 10232036, 15479600
Offset: 1

Views

Author

R. H. Hardin, Oct 23 2015

Keywords

Examples

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

Links

Crossrefs

Column 3 of A263693.

Formula

Empirical: a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) for n>12.
Empirical g.f.: x*(1 + x + 3*x^2 + 17*x^3 - 11*x^4 - 20*x^5 + 6*x^6 - 8*x^7 + 2*x^9 - 4*x^10 - 4*x^11) / (1 - x - x^2 + x^3 - x^4). - Colin Barker, Jan 02 2019
Showing 1-3 of 3 results.

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