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 1-4 of 4 results.

A223599 T(n,k)=Petersen graph (8,2) coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph.

Original entry on oeis.org

16, 48, 256, 144, 256, 4096, 432, 1504, 1376, 65536, 1296, 6736, 16192, 7424, 1048576, 3888, 32768, 122608, 176224, 40160, 16777216, 11664, 156592, 1124064, 2372080, 1931968, 217600, 268435456, 34992, 755200, 9902320, 43725920, 47659632
Offset: 1

Views

Author

R. H. Hardin Mar 23 2013

Keywords

Comments

Table starts
............16........48..........144.............432...............1296
...........256.......256.........1504............6736..............32768
..........4096......1376........16192..........122608............1124064
.........65536......7424.......176224.........2372080...........43725920
.......1048576.....40160......1931968........47659632.........1807461152
......16777216....217600.....21308000.......982848688........77164934624
.....268435456...1180256....236213312.....20631729648......3355919411936
....4294967296...6405888...2629972704....438231627440....147579242411936
...68719476736..34782688..29389265856...9379905920496...6534353238114336
.1099511627776.188912640.329426847840.201754894742320.290550417324168160

Examples

			Some solutions for n=3 k=4
.14..6..5.13...13.15..9.15...12..4.12.10....6..5.13.15....8.14..8.10
..7..6..5..6...13.15..9..1...12..4.12..4....6..5.13..5....8.14..8.14
..5..6.14..6....9.15..9.11....5..4.12.14...13..5..6..5....6.14..6.14

Links

Crossrefs

Column 1 is A001025
Column 2 is A223434
Row 1 is A188825(n+1)

Formula

Empirical for column k:
k=1: a(n) = 16*a(n-1)
k=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3)
k=3: a(n) = 23*a(n-1) -153*a(n-2) +217*a(n-3) +258*a(n-4) -456*a(n-5) -104*a(n-6) +192*a(n-7)
k=4: [order 9]
k=5: [order 29]
k=6: [order 55]
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 6*a(n-1) +3*a(n-2) -42*a(n-3) -8*a(n-4) +48*a(n-5) for n>6
n=3: [order 11] for n>12
n=4: [order 28] for n>29
n=5: [order 74] for n>75

A223692 T(n,k)=Petersen graph (8,2) coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph.

Original entry on oeis.org

16, 48, 256, 144, 432, 4096, 432, 2304, 3888, 65536, 1296, 12384, 37008, 34992, 1048576, 3888, 66816, 363600, 595584, 314928, 16777216, 11664, 361440, 3788640, 10817856, 9594000, 2834352, 268435456, 34992, 1958400, 40075632, 223096320, 324280368, 154616832, 25509168, 4294967296
Offset: 1

Views

Author

R. H. Hardin, Mar 25 2013

Keywords

Examples

			Table starts:
          16,        48,         144,           432,             1296, ...
         256,       432,        2304,         12384,            66816, ...
        4096,      3888,       37008,        363600,          3788640, ...
       65536,     34992,      595584,      10817856,        223096320, ...
     1048576,    314928,     9594000,     324280368,      13402129824, ...
    16777216,   2834352,   154616832,    9762152544,     814399853760, ...
   268435456,  25509168,  2492365968,  294583794768,   49817845241568, ...
  4294967296, 229582512, 40180445568, 8901308553408, 3059068970173824, ...
Some solutions for n=3 k=4
..2..1..9..1....6..5..4..5....6.14..6.14....4..3..2.10....2..3..4..3
..2..1..9.11....4..5..6.14...12.14..8.14....2.10..2.10....4..3.11.13
..9.11..9.15....6..7..6.14....8..0..8..0....8.10..8.10...11.13.11..9

Links

Crossrefs

Column 1 is A001025
Column 2 is 48*9^(n-1)
Row 1 is A188825(n+1)

Formula

Empirical for column k:
k=1: a(n) = 16*a(n-1)
k=2: a(n) = 9*a(n-1)
k=3: a(n) = 24*a(n-1) -127*a(n-2)
k=4: a(n) = 59*a(n-1) -1103*a(n-2) +7621*a(n-3) -16900*a(n-4)
k=5: [order 7] for n>8
k=6: [order 17] for n>18
k=7: [order 37] for n>39
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3) for n>4
n=3: a(n) = [order 10] for n>12
n=4: a(n) = [order 24] for n>27
n=5: a(n) = [order 56] for n>61

A223440 T(n,k)=Generalized Petersen graph (8,2) coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

16, 48, 48, 144, 256, 144, 432, 1376, 1376, 432, 1296, 7424, 14112, 7424, 1296, 3888, 40160, 147520, 147520, 40160, 3888, 11664, 217600, 1562176, 3099264, 1562176, 217600, 11664, 34992, 1180256, 16693920, 67182208, 67182208, 16693920, 1180256
Offset: 1

Views

Author

R. H. Hardin Mar 20 2013

Keywords

Comments

Table starts
.....16........48..........144.............432...............1296
.....48.......256.........1376............7424..............40160
....144......1376........14112..........147520............1562176
....432......7424.......147520.........3099264...........67182208
...1296.....40160......1562176........67182208.........3049973040
...3888....217600.....16693920......1485628224.......142702806112
..11664...1180256....179532768.....33277934848......6790055219264
..34992...6405888...1939216640....751557814208....326095786136512
.104976..34782688..21008925952..17060996532992..15740601974728144
.314928.188912640.228065409888.388541047749184.761894144429277728

Examples

			Some solutions for n=3 k=4
..7.15..7..0....1..0..7..0...10..8.14.12....8.14.12.10....9..1..9.11
..6..7..6..7....2..1..0..7...12.10.12.14...14.12.10..8....1..9.11..9
..7.15..7.15...10..2..1..0...14..8.14..8....8.14.12.14....9..1..9..1

Links

Crossrefs

Column 1 is A188825(n+1)

Formula

Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3)
k=3: a(n) = 15*a(n-1) -18*a(n-2) -310*a(n-3) +167*a(n-4) +475*a(n-5) -244*a(n-6) -100*a(n-7) +48*a(n-8)
k=4: [order 14]
k=5: [order 36]
k=6: [order 75]

A291873 Array read by antidiagonals: T(m,n) = number of connected dominating sets in the m X n king graph.

Original entry on oeis.org

1, 3, 3, 4, 15, 4, 4, 48, 48, 4, 4, 144, 336, 144, 4, 4, 432, 2192, 2192, 432, 4, 4, 1296, 14544, 29648, 14544, 1296, 4, 4, 3888, 96528, 405648, 405648, 96528, 3888, 4, 4, 11664, 640336, 5568336, 11293568, 5568336, 640336, 11664, 4
Offset: 1

Views

Author

Andrew Howroyd, Sep 04 2017

Keywords

Examples

			Array begins:
======================================================================
m\n| 1    2      3        4          5             6               7
---|------------------------------------------------------------------
1  | 1    3      4        4          4             4               4...
2  | 3   15     48      144        432          1296            3888...
3  | 4   48    336     2192      14544         96528          640336...
4  | 4  144   2192    29648     405648       5568336        76414224...
5  | 4  432  14544   405648   11293568     315156544      8793207424...
6  | 4 1296  96528  5568336  315156544   17784998912   1001953789632...
7  | 4 3888 640336 76414224 8793207424 1001953789632 113637188081536...
...

Links

Crossrefs

Row 2 is A188825(n) for n > 2.
Main diagonal is A289180.
Cf. A218663, A291872.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.