A270145 Number of n X 2 0..7 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling seven exactly once.

8, 1440, 85056, 4126368, 182257536, 7623445344, 307704553920, 12111206870304, 467855602824192, 17813625850002144, 670485480935347776, 25000461221001205920, 924950147066819934336, 33996076829066361534048

Offset

1,1

Links

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

Formula

Empirical: a(n) = 66*a(n-1) - 1021*a(n-2) - 2244*a(n-3) - 1156*a(n-4) for n>5.

Conjectures from Colin Barker, Jan 30 2019: (Start)

G.f.: 8*x*(1 - x)^2*(1 + 116*x + 4*x^2) / ((1 + x)^2*(1 - 34*x)^2).

a(n) = (48*(-383214*(-1)^n - 2660911*34^n + 35*(363562*(-1)^n + 115797*34^n)*n)) / 210644875 for n>1.

(End)

Example

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

Crossrefs

Column 2 of A270150.

Sequence in context: A064073 A282889 A225068 * A201492 A172938 A252176

Adjacent sequences: A270142 A270143 A270144 * A270146 A270147 A270148

Keyword

nonn

Author

R. H. Hardin, Mar 12 2016

Status

approved