A223506 Petersen graph (3,1) coloring a rectangular array: number of 3 X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

36, 121, 1519, 16323, 182901, 2030665, 22598167, 251348043, 2795984857, 31101456601, 345963177427, 3848382739711, 42808185822221, 476184598157809, 5296925638013539, 58921311528252323, 655421879453116645

Offset

1,1

Comments

Row 3 of A223504.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 4*a(n-2) - 73*a(n-3) + 103*a(n-4) - 23*a(n-5) - 16*a(n-6) + 4*a(n-7) for n>8.

Empirical g.f.: x*(36 - 311*x + 211*x^2 + 1207*x^3 - 1774*x^4 + 397*x^5 + 272*x^6 - 68*x^7) / (1 - 12*x + 4*x^2 + 73*x^3 - 103*x^4 + 23*x^5 + 16*x^6 - 4*x^7). - Colin Barker, Aug 21 2018

Example

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

Crossrefs

Cf. A223504.

Sequence in context: A278022 A333007 A016862 * A238037 A238032 A365506

Adjacent sequences: A223503 A223504 A223505 * A223507 A223508 A223509

Keyword

nonn

Author

R. H. Hardin, Mar 21 2013

Status

approved