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 1-6 of 6 results.

A201040 Number of -6..6 arrays of n elements with adjacent element differences also in -6..6.

Original entry on oeis.org

13, 127, 1287, 13021, 131781, 1333683, 13497523, 136601483, 1382473365, 13991301963, 141598771951, 1433048351749, 14503145402825, 146778876175813, 1485473522677393, 15033713597401013, 152148484020986879
Offset: 1

Views

Author

R. H. Hardin, Nov 26 2011

Keywords

Comments

Column 6 of A201042.

Examples

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

Links

Crossrefs

Cf. A201042.

Formula

Empirical: a(n) = 10*a(n-1) +3*a(n-2) -18*a(n-3) -a(n-4) +8*a(n-5) -a(n-7).
Empirical g.f.: x*(13 - 3*x - 22*x^2 + 4*x^3 + 9*x^4 - x^5 - x^6) / ((1 - x)*(1 - 9*x - 12*x^2 + 6*x^3 + 7*x^4 - x^5 - x^6)). - Colin Barker, May 21 2018

A201041 Number of -7..7 arrays of n elements with adjacent element differences also in -7..7.

Original entry on oeis.org

15, 169, 1975, 23045, 268983, 3139529, 36644243, 427707523, 4992154799, 58267877227, 680096201983, 7938007456913, 92651542829899, 1081418534229055, 12622197218251193, 147324886317031649, 1719559736948358761
Offset: 1

Views

Author

R. H. Hardin Nov 26 2011

Keywords

Comments

Column 7 of A201042

Examples

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

Links

Formula

Empirical: a(n) = 11*a(n-1) +10*a(n-2) -24*a(n-3) -15*a(n-4) +13*a(n-5) +7*a(n-6) -2*a(n-7) -a(n-8)

A201043 Number of -n..n arrays of 4 elements with adjacent element differences also in -n..n.

Original entry on oeis.org

41, 295, 1111, 3011, 6691, 13021, 23045, 37981, 59221, 88331, 127051, 177295, 241151, 320881, 418921, 537881, 680545, 849871, 1048991, 1281211, 1550011, 1859045, 2212141, 2613301, 3066701, 3576691, 4147795, 4784711, 5492311, 6275641
Offset: 1

Views

Author

R. H. Hardin, Nov 26 2011

Keywords

Comments

Row 4 of A201042.

Examples

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

Links

Crossrefs

Cf. A201042.

Formula

Empirical: a(n) = (29/4)*n^4 + (29/2)*n^3 + (51/4)*n^2 + (11/2)*n + 1.
Conjectures from Colin Barker, May 21 2018: (Start)
G.f.: x*(41 + 90*x + 46*x^2 - 4*x^3 + 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)

A201044 Number of -n..n arrays of 5 elements with adjacent element differences also in -n..n.

Original entry on oeis.org

99, 1161, 6083, 21141, 57343, 131781, 268983, 502265, 875083, 1442385, 2271963, 3445805, 5061447, 7233325, 10094127, 13796145, 18512627, 24439129, 31794867, 40824069, 51797327, 65012949, 80798311, 99511209, 121541211, 147311009
Offset: 1

Views

Author

R. H. Hardin, Nov 26 2011

Keywords

Comments

Row 5 of A201042.

Examples

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

Links

Crossrefs

Cf. A201042.

Formula

Empirical: a(n) = (169/15)*n^5 + (169/6)*n^4 + 32*n^3 + (119/6)*n^2 + (101/15)*n + 1.
Conjectures from Colin Barker, May 22 2018: (Start)
G.f.: x*(99 + 567*x + 602*x^2 + 78*x^3 + 7*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A201045 Number of -n..n arrays of 6 elements with adjacent element differences also in -n..n.

Original entry on oeis.org

239, 4569, 33305, 148433, 491429, 1333683, 3139529, 6641881, 12930475, 23552717, 40627137, 66969449, 106231217, 163051127, 243218865, 353851601, 503583079, 702765313, 963682889, 1300779873, 1730899325, 2273535419, 2951098169
Offset: 1

Views

Author

R. H. Hardin, Nov 26 2011

Keywords

Comments

Row 6 of A201042.

Examples

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

Links

Crossrefs

Cf. A201042.

Formula

Empirical: a(n) = (2101/120)*n^6 + (2101/40)*n^5 + (1753/24)*n^4 + (1405/24)*n^3 + (569/20)*n^2 + (119/15)*n + 1.
Conjectures from Colin Barker, May 22 2018: (Start)
G.f.: x*(239 + 2896*x + 6341*x^2 + 2882*x^3 + 253*x^4 - 6*x^5 + x^6) / (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>7.
(End)

A201046 Number of -n..n arrays of 7 elements with adjacent element differences also in -n..n.

Original entry on oeis.org

577, 17981, 182349, 1042167, 4211559, 13497523, 36644243, 87831605, 191065045, 384593857, 726495089, 1301560155, 2229621291, 3675454983, 5860399495, 9075823625, 13698583817, 20208606757, 29208734581, 41446969823, 57841257231
Offset: 1

Views

Author

R. H. Hardin, Nov 26 2011

Keywords

Comments

Row 7 of A201042.

Examples

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

Links

Crossrefs

Cf. A201042.

Formula

Empirical: a(n) = (17141/630)*n^7 + (17141/180)*n^6 + (28177/180)*n^5 + (2759/18)*n^4 + (17299/180)*n^3 + (6929/180)*n^2 + (1921/210)*n + 1.
Conjectures from Colin Barker, May 22 2018: (Start)
G.f.: x*(577 + 13365*x + 54657*x^2 + 54531*x^3 + 13449*x^4 + 541*x^5 + 9*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
Showing 1-6 of 6 results.

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