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 1-7 of 7 results.

A183883 Number of arrangements of n+2 numbers in 0..8 with each number being the sum mod 9 of two others.

Original entry on oeis.org

1, 31, 1761, 75451, 1598395, 23327655, 275846173, 2895194179, 28388585391, 267809160367, 2472279047473, 22552186971627, 204400652073763, 1846262280059767, 16646854130219781, 149959684159252819
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 8 of A183884

Examples

			Some solutions for n=2
..6....3....0....6....0....6....3....3....3....6....3....6....3....3....6....6
..6....0....0....0....6....3....3....6....3....3....6....3....6....0....0....6
..3....6....0....3....6....0....6....0....6....0....3....6....6....6....3....3
..0....3....0....6....3....3....6....3....0....6....0....3....0....6....3....3

Links

A183877 Number of arrangements of n+2 numbers in 0..2 with each number being the sum mod 3 of two others.

Original entry on oeis.org

1, 31, 171, 631, 2059, 6399, 19483, 58807, 176859, 531103, 1593931, 4782519, 14348395, 43046143, 129139515, 387419767, 1162260667, 3486783519, 10460352235, 31381058551, 94143177675, 282429535231, 847288608091, 2541865826871
Offset: 1

Views

Author

R. H. Hardin, Jan 07 2011

Keywords

Examples

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

Links

Crossrefs

Column 2 of A183884.

Programs

  • Maple
    1, seq(3^(n+2)-2*(n+3)^2, n=2..30); # Robert Israel, Sep 30 2018

Formula

Empirical (for n>=2): 3^(n+2) - 2*(n+3)^2. - Vaclav Kotesovec, Nov 27 2012
Conjectures from Colin Barker, Apr 05 2018: (Start)
G.f.: x*(1 + 25*x - 3*x^2 - 33*x^3 + 18*x^4) / ((1 - x)^3*(1 - 3*x)).
a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4) for n>5.
(End)
Conjecture is true. The complement consists of arrangements of the forms
1*, 2*, 01*, 02*, 10*, 12*, 20*, 21*, 001*, 002* and 120*. Robert Israel, Sep 30 2018

A183878 Number of arrangements of n+2 numbers in 0..3 with each number being the sum mod 4 of two others.

Original entry on oeis.org

4, 35, 446, 2827, 13686, 59859, 250198, 1023347, 4140830, 16663627, 66867438, 267922683, 1072654438, 4292666147, 17175010598, 68709242467, 274856398542, 1099466524251, 4397952122110, 17591988892331, 70368333113174
Offset: 1

Views

Author

R. H. Hardin, Jan 07 2011

Keywords

Comments

Column 3 of A183884.

Examples

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

Links

Crossrefs

Cf. A183884.

Formula

Empirical (for n>=3): 4^(n+2) - (2*n+7)*2^(n+2) - 2*n^3 - 9*n^2 - 10*n + 3. - Vaclav Kotesovec, Nov 27 2012
Conjectures from Colin Barker, Apr 05 2018: (Start)
G.f.: x*(4 - 13*x + 258*x^2 - 1087*x^3 + 1318*x^4 + 444*x^5 - 2040*x^6 + 1536*x^7 - 384*x^8) / ((1 - x)^4*(1 - 2*x)^2*(1 - 4*x)).
a(n) = 12*a(n-1) - 58*a(n-2) + 148*a(n-3) - 217*a(n-4) + 184*a(n-5) - 84*a(n-6) + 16*a(n-7) for n>9.
(End)

A183879 Number of arrangements of n+2 numbers in 0..4 with each number being the sum mod 5 of two others.

Original entry on oeis.org

1, 25, 821, 8361, 57625, 336617, 1817149, 9433849, 48036737, 242284857, 1216409221, 6093687497, 30495285865, 152537717449, 762827288141, 3814448005209, 19072935346513, 95366219539097, 476834503269013
Offset: 1

Views

Author

R. H. Hardin, Jan 07 2011

Keywords

Comments

Column 4 of A183884.

Examples

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

Links

Crossrefs

Cf. A183884.

Formula

Empirical (for n>=2): 5^(n+2) - (10*n^2+70*n+124)*2^n + 2*(3*n+8)*(n^2+5*n+8). - Vaclav Kotesovec, Nov 27 2012
Conjectures from Colin Barker, Apr 05 2018: (Start)
G.f.: x*(1 + 10*x + 538*x^2 - 1960*x^3 + 701*x^4 + 4706*x^5 - 7204*x^6 + 4312*x^7 - 960*x^8) / ((1 - x)^4*(1 - 2*x)^3*(1 - 5*x)).
a(n) = 15*a(n-1) - 92*a(n-2) + 306*a(n-3) - 609*a(n-4) + 747*a(n-5) - 554*a(n-6) + 228*a(n-7) - 40*a(n-8) for n>9.
(End)

A183880 Number of arrangements of n+2 numbers in 0..5 with each number being the sum mod 6 of two others.

Original entry on oeis.org

4, 89, 1566, 20527, 183310, 1347565, 8984158, 56952323, 351661806, 2141759809, 12950960686, 78020943223, 469112191342, 2817757426037, 16916183927550, 101527228990219, 609257523135022, 3655839340823305, 21935955102434638
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 5 of A183884

Examples

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

Links

A183881 Number of arrangements of n+2 numbers in 0..6 with each number being the sum mod 7 of two others.

Original entry on oeis.org

1, 1, 1231, 32521, 424537, 4079713, 33702403, 257404033, 1885866973, 13515603289, 95750388631, 674299155193, 4734193668289, 33187816266097, 232479450595819, 1627911123290065, 11397233380815013, 79786797746740777, 558527947985495935
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 6 of A183884

Examples

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

Links

A183882 Number of arrangements of n+2 numbers in 0..7 with each number being the sum mod 8 of two others.

Original entry on oeis.org

4, 35, 1986, 52827, 885690, 10540371, 104446714, 938543435, 7996169226, 66170227587, 538977760842, 4352945018619, 34996920361210, 280699272183347, 2248598404709850, 18001206351037995, 144060870372238122
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 7 of A183884

Examples

			Some solutions for n=2
..6....6....2....2....0....2....6....4....4....4....6....4....6....6....4....2
..6....2....6....6....4....4....6....4....0....2....4....0....2....2....6....6
..4....2....4....6....0....6....2....0....4....2....2....4....6....4....6....2
..2....4....2....4....4....2....4....0....0....6....6....4....4....2....2....4

Links

Showing 1-7 of 7 results.

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