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.

A183885 Number of arrangements of n+3 numbers in 0..2 with each number being the sum mod 3 of three others.

Original entry on oeis.org

1, 121, 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

Comments

Column 2 of A183892.

Examples

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

Links

Crossrefs

Cf. A183892.

Formula

Empirical (for n>=3): 3^(n+3) - 2*(n+4)^2. - Vaclav Kotesovec, Nov 27 2012
Conjectures from Colin Barker, Apr 05 2018: (Start)
G.f.: x*(1 + 115*x - 83*x^2 - 285*x^3 + 410*x^4 - 150*x^5) / ((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>6.
(End)

A183886 Number of arrangements of n+3 numbers in 0..3 with each number being the sum mod 4 of three others.

Original entry on oeis.org

16, 292, 2574, 13344, 59518, 250124, 1024174, 4143944, 16671934, 66886900, 267965390, 1072744752, 4292852990, 17175392028, 68710014830, 274857954776, 1099469650494, 4397958390916, 17592001449102, 70368358249024
Offset: 1

Views

Author

R. H. Hardin, Jan 07 2011

Keywords

Comments

Column 3 of A183892.

Examples

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

Links

Crossrefs

Cf. A183892.

Formula

Empirical (for n>=2): 4^(n+3) - (n+3)*2^(n+4) - 2/3*(7*n^3+51*n^2+125*n+108). - Vaclav Kotesovec, Nov 27 2012.
Conjectures from Colin Barker, Apr 05 2018: (Start)
G.f.: 2*x*(8 + 50*x - x^2 - 1488*x^3 + 4469*x^4 - 5336*x^5 + 2996*x^6 - 656*x^7) / ((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>8.
(End)

A183887 Number of arrangements of n+3 numbers in 0..4 with each number being the sum mod 5 of three others.

Original entry on oeis.org

1, 241, 8681, 63645, 363749, 1905097, 9681073, 48678653, 243871365, 1220204441, 6102563585, 30515709437, 152584140357, 762931805705, 3814681507825, 19073453656861, 95367363682085, 476837016657945, 2384185496162945
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 4 of A183892

Examples

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

Links

A183888 Number of arrangements of n+3 numbers in 0..5 with each number being the sum mod 6 of three others.

Original entry on oeis.org

8, 982, 20152, 201154, 1466628, 9469778, 58702904, 357576342, 2161032260, 13012476622, 78214995120, 469720252818, 2819655668996, 16922097475386, 101545629217608, 609314732885086, 3656017115990916, 21936507241621846
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 5 of A183892

Examples

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

Links

A183889 Number of arrangements of n+3 numbers in 0..6 with each number being the sum mod 7 of three others.

Original entry on oeis.org

1, 1, 32821, 542557, 4978219, 38280865, 277198249, 1964161189, 13808869207, 96809981737, 678032111797, 4747103957005, 33231843226435, 232627950507697, 1628407600271233, 11398881253796341, 79792234154371567, 558545790385795897
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 6 of A183892

Examples

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

Links

A183890 Number of arrangements of n+3 numbers in 0..7 with each number being the sum mod 8 of three others.

Original entry on oeis.org

16, 492, 57614, 1172880, 13388190, 122033732, 1030189438, 8431580544, 68127437030, 547474985956, 4389023189750, 35147929076368, 281325633652942, 2251182017398052, 18011828552749070, 144104466144893120
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 7 of A183892

Examples

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

Links

A183891 Number of arrangements of n+3 numbers in 0..8 with each number being the sum mod 9 of three others.

Original entry on oeis.org

1, 241, 81751, 2466535, 34099017, 356237575, 3382161175, 31040377215, 281338882705, 2538405887395, 22865861038983, 205856624277475, 1852911128126185, 16676836226840751, 150093537945401959
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 8 of A183892

Examples

			Some solutions for n=2
..0....3....3....0....8....6....0....3....1....6....3....6....6....3....6....0
..3....6....3....3....6....8....6....6....3....0....6....3....2....1....6....3
..6....0....3....3....2....2....6....0....7....6....3....3....8....4....3....6
..6....6....0....6....6....6....3....6....3....3....0....3....6....7....0....6
..6....6....6....3....5....5....0....0....4....0....0....0....5....3....0....0

Links

Showing 1-7 of 7 results.

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