A223423 -id:A223423 - cp's OEIS frontend

A223416 3-level binary fanout graph coloring a rectangular array: number of n X n 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

7, 40, 868, 47872, 9210784, 4565849088, 7939011165696, 35771349106229248, 568805952799804981248, 23519412222495212487835648, 3445579826336104496385828585472, 1315514651265664243430976739562487808

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Diagonal of A223423

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

R. H. Hardin, Table of n, a(n) for n = 1..16

A223417 3-level binary fanout graph coloring a rectangular array: number of nX1 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

7, 12, 26, 48, 104, 192, 416, 768, 1664, 3072, 6656, 12288, 26624, 49152, 106496, 196608, 425984, 786432, 1703936, 3145728, 6815744, 12582912, 27262976, 50331648, 109051904, 201326592, 436207616, 805306368, 1744830464, 3221225472

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Column 1 of A223423

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 4*a(n-2) for n>3

A223418 3-level binary fanout graph coloring a rectangular array: number of n X 3 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

26, 136, 868, 4720, 29912, 163168, 1033328, 5638336, 35704800, 194827648, 1233740224, 6732071680, 42630619008, 232619832832, 1473057249024, 8037939530752, 50899980869120, 277742748522496, 1758796582951936

Offset: 1

R. H. Hardin, Mar 20 2013

nonn

Column 3 of A223423.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A223423.

Empirical: a(n) = 38*a(n-2) - 120*a(n-4) + 32*a(n-6).

Empirical g.f.: 2*x*(13 + 68*x - 60*x^2 - 224*x^3 + 24*x^4 + 64*x^5) / (1 - 38*x^2 + 120*x^4 - 32*x^6). - Colin Barker, Aug 20 2018

A223419 3-level binary fanout graph coloring a rectangular array: number of n X 4 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

48, 464, 4720, 47872, 486016, 4934272, 50097024, 508632832, 5164146176, 52431620096, 532338988032, 5404846559232, 54875501465600, 557151943860224, 5656773689024512, 57433325141737472, 583121585796284416

Offset: 1

R. H. Hardin, Mar 20 2013

nonn

Column 4 of A223423.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A223423.

Empirical: a(n) = 14*a(n-1) - 36*a(n-2) - 40*a(n-3) + 88*a(n-4) + 32*a(n-5) - 32*a(n-6).

Empirical g.f.: 16*x*(3 - 13*x - 3*x^2 + 26*x^3 + 4*x^4 - 8*x^5) / (1 - 14*x + 36*x^2 + 40*x^3 - 88*x^4 - 32*x^5 + 32*x^6). - Colin Barker, Aug 20 2018

A223420 3-level binary fanout graph coloring a rectangular array: number of nX5 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

104, 1584, 29912, 486016, 9210784, 150006016, 2844612736, 46345527296, 878977950208, 14321836797952, 271631946213376, 4425979070611456, 83944852851777536, 1367805247361974272, 25942363680265961472

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Column 5 of A223423

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 392*a(n-2) -26768*a(n-4) +353408*a(n-6) -1274624*a(n-8) +1441792*a(n-10) -307200*a(n-12) for n>13

A223421 3-level binary fanout graph coloring a rectangular array: number of nX6 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

192, 5408, 163168, 4934272, 150006016, 4565849088, 139114196992, 4240305623040, 129279082045440, 3941937218551808, 120203880286208000, 3665566262474506240, 111781755512338644992, 3408823463373890650112, 103953721139031970938880

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Column 6 of A223423

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 48*a(n-1) -460*a(n-2) -4144*a(n-3) +60160*a(n-4) -27456*a(n-5) -1549312*a(n-6) +3687168*a(n-7) +10996224*a(n-8) -43337728*a(n-9) -1603584*a(n-10) +149012480*a(n-11) -140541952*a(n-12) -92667904*a(n-13) +182190080*a(n-14) -52166656*a(n-15) -28835840*a(n-16) +16777216*a(n-17) -2097152*a(n-18)

A223422 3-level binary fanout graph coloring a rectangular array: number of nX7 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

416, 18464, 1033328, 50097024, 2844612736, 139114196992, 7939011165696, 389154431528960, 22244132907945984, 1091144538683604992, 62401586754017968128, 3061680318925083639808, 175122575873489263525888

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Column 7 of A223423

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 4144*a(n-2) -4233568*a(n-4) +1423446528*a(n-6) -216571051008*a(n-8) +17498453049344*a(n-10) -823976834072576*a(n-12) +23806610175950848*a(n-14) -433179956841807872*a(n-16) +5014404982720430080*a(n-18) -36922985056839925760*a(n-20) +171827754849678655488*a(n-22) -499189157380780720128*a(n-24) +886405116754355290112*a(n-26) -927140136557417070592*a(n-28) +537868927709415997440*a(n-30) -158472804425401368576*a(n-32) +20342196566879109120*a(n-34) -788129934789836800*a(n-36)

cp's OEIS Frontend

A223416 3-level binary fanout graph coloring a rectangular array: number of n X n 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

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A223417 3-level binary fanout graph coloring a rectangular array: number of nX1 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

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A223418 3-level binary fanout graph coloring a rectangular array: number of n X 3 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

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A223419 3-level binary fanout graph coloring a rectangular array: number of n X 4 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

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A223420 3-level binary fanout graph coloring a rectangular array: number of nX5 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

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A223421 3-level binary fanout graph coloring a rectangular array: number of nX6 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

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A223422 3-level binary fanout graph coloring a rectangular array: number of nX7 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

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