A270145 - OEIS

%I #9 Jan 30 2019 06:21:29

%S 8,1440,85056,4126368,182257536,7623445344,307704553920,

%T 12111206870304,467855602824192,17813625850002144,670485480935347776,

%U 25000461221001205920,924950147066819934336,33996076829066361534048

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

%H R. H. Hardin, <a href="/A270145/b270145.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Jan 30 2019: (Start)

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

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

%F (End)

%e Some solutions for n=3:

%e ..5..0. .3..3. .7..3. .2..2. .2..3. .5..7. .6..5. .5..3. .3..6. .6..3

%e ..1..0. .0..7. .6..5. .4..3. .1..0. .4..3. .6..6. .4..1. .2..1. .4..0

%e ..6..5. .1..1. .2..6. .7..6. .4..6. .7..5. .3..4. .5..5. .3..1. .0..2

%Y Column 2 of A270150.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 12 2016