A220567 Number of ways to reciprocally link elements of an 6Xn array either to themselves or to exactly one horizontal or antidiagonal neighbor

1, 233, 6076, 338581, 14298089, 665748170, 29955561052, 1363847439227, 61845935792336, 2808292682072854, 127461441592952329, 5786012622635830257, 262638882187378528534, 11921898805633926722093, 541164958214032363841199

Offset

1,2

Comments

Row 6 of A220562

Links

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

Formula

Empirical: a(n) = 13*a(n-1) +1348*a(n-2) +10654*a(n-3) -198504*a(n-4) -1906076*a(n-5) +16144268*a(n-6) +135853346*a(n-7) -925177576*a(n-8) -4891188529*a(n-9) +35999318281*a(n-10) +81980396412*a(n-11) -848296316904*a(n-12) -276758340388*a(n-13) +11227641980488*a(n-14) -7107958733596*a(n-15) -92787258095632*a(n-16) +107881224287236*a(n-17) +525583351897147*a(n-18) -774675289613655*a(n-19) -2182902615756840*a(n-20) +3555500220788694*a(n-21) +6973910104740084*a(n-22) -11426713159097796*a(n-23) -17667940720548336*a(n-24) +26747813225197794*a(n-25) +35945989169311476*a(n-26) -46394604844529149*a(n-27) -58560503957694547*a(n-28) +59946651607436776*a(n-29) +75473026016657552*a(n-30) -57619701988418728*a(n-31) -75893814357642448*a(n-32) +40983675195728936*a(n-33) +58931290214948032*a(n-34) -21385512054198856*a(n-35) -35152757210761395*a(n-36) +8057875480743783*a(n-37) +16091164614749124*a(n-38) -2117225467318182*a(n-39) -5658108579422624*a(n-40) +352030436802844*a(n-41) +1530178310024236*a(n-42) -22441127837162*a(n-43) -318296736753680*a(n-44) -5136539584403*a(n-45) +50823610079499*a(n-46) +1734560714908*a(n-47) -6199297816488*a(n-48) -263242733620*a(n-49) +572842763656*a(n-50) +25065179764*a(n-51) -39590221744*a(n-52) -1591760572*a(n-53) +2008410297*a(n-54) +67587747*a(n-55) -72760800*a(n-56) -1863630*a(n-57) +1806100*a(n-58) +31300*a(n-59) -28744*a(n-60) -282*a(n-61) +260*a(n-62) +a(n-63) -a(n-64)

Example

Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
..0..7..7....0..0..0....6..4..7....0..7..0....0..7..0....0..0..0....0..6..4
..3..3..0....6..4..0....0..3..0....3..6..4....3..7..0....6..4..0....6..4..7
..6..4..0....0..6..4....0..6..4....6..4..0....3..0..0....0..0..0....0..3..0
..0..0..0....6..4..7....6..4..0....0..7..0....0..7..0....0..0..0....0..0..7
..0..7..0....0..3..0....0..6..4....3..7..0....3..7..7....0..0..7....0..3..0
..3..0..0....0..6..4....0..6..4....3..6..4....3..3..0....0..3..0....6..4..0

Crossrefs

Sequence in context: A221812 A219065 A301956 * A201035 A189454 A201834

Adjacent sequences: A220564 A220565 A220566 * A220568 A220569 A220570

Keyword

nonn

Author

R. H. Hardin Dec 16 2012

Status

approved