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Number of (n+2)X(2+2) 0..1 arrays with each row and column not divisible by 5, read as a binary number with top and left being the most significant bits.
1

%I #4 Oct 08 2015 07:52:45

%S 512,6928,92472,1198816,14394128,174159952,2100720600,25327918144,

%T 303937235408,3649959544336,43807632440376,525844497250336,

%U 6310134549806480,75726848781701584,908720872928731032

%N Number of (n+2)X(2+2) 0..1 arrays with each row and column not divisible by 5, read as a binary number with top and left being the most significant bits.

%C Column 2 of A263040.

%H R. H. Hardin, <a href="/A263034/b263034.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) -52*a(n-2) +440*a(n-3) +1940*a(n-4) -42136*a(n-5) +130832*a(n-6) -1272928*a(n-7) +234026*a(n-8) +34403252*a(n-9) -63189880*a(n-10) +952057808*a(n-11) -516283820*a(n-12) -10970711960*a(n-13) +9550612240*a(n-14) -282398311520*a(n-15) +96140026255*a(n-16) +1404615957550*a(n-17) -501871284980*a(n-18) +34714525551160*a(n-19) -5440122625184*a(n-20) -68377213321664*a(n-21) +6191483638912*a(n-22) -1653436086997760*a(n-23) +68472989925120*a(n-24) +824525429054976*a(n-25) -5699099907072*a(n-26) +19800008497133568*a(n-27) -63128491278336*a(n-28) -757541895340032*a(n-29) -18181005488160768*a(n-31)

%e Some solutions for n=3

%e ..0..1..1..1....0..1..0..0....1..1..0..0....0..1..1..0....0..0..1..0

%e ..0..0..1..0....1..0..0..1....1..0..1..1....1..0..1..1....1..1..0..1

%e ..1..1..0..0....0..1..1..1....0..0..1..1....1..1..0..0....1..1..0..0

%e ..0..1..0..0....0..1..1..0....1..1..0..0....1..0..1..1....0..1..1..1

%e ..0..1..0..0....1..1..0..0....1..1..0..0....0..1..1..1....0..0..0..1

%Y Cf. A263040.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 08 2015