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Number of (5+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 5, read as a binary number with top and left being the most significant bits.
1

%I #4 Sep 23 2015 18:54:34

%S 13,37,469,2413,30229,234421,2924245,29005981,362253013,4077093157,

%T 51105791029,611509849933,7700348530069,94992216728341,

%U 1201803227962645,15070500857186941,191509623622912213,2424933117697177477

%N Number of (5+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 5, read as a binary number with top and left being the most significant bits.

%C Row 5 of A262472.

%H R. H. Hardin, <a href="/A262475/b262475.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 13*a(n-1) +598*a(n-2) -7774*a(n-3) -159204*a(n-4) +2069652*a(n-5) +25102262*a(n-6) -326329406*a(n-7) -2625721997*a(n-8) +34134385961*a(n-9) +193137936456*a(n-10) -2510793173928*a(n-11) -10320305833888*a(n-12) +134163975840544*a(n-13) +407697970217164*a(n-14) -5300073612823132*a(n-15) -11991972387294603*a(n-16) +155895641034829839*a(n-17) +262231592584367494*a(n-18) -3409010703596777422*a(n-19) -4220509269410999212*a(n-20) +54866620502342989756*a(n-21) +49009303645963174686*a(n-22) -637120947397521270918*a(n-23) -397172035135043236199*a(n-24) +5163236456755562070587*a(n-25) +2128419673029471315452*a(n-26) -27669455749383127100876*a(n-27) -6888351482794359567696*a(n-28) +89548569276326674380048*a(n-29) +11351034044825782285888*a(n-30) -147563442582735169716544*a(n-31) -6238969631490801587200*a(n-32) +81106605209380420633600*a(n-33)

%e Some solutions for n=4

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

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

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

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

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

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

%Y Cf. A262472.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 23 2015