A183778 - OEIS

%I #10 Jan 09 2025 15:43:55

%S 32,217,1969,15887,136843,1146964,9764363,82573675,701022093,

%T 5941108591,50402814448,427394109663,3625210947353,30744778516059,

%U 260766196940447,2211608594540996,18757714441639535,159090037814462703,1349309620582616393,11443973193607153699,97060893025685775328

%N Half the number of (n+1) X 6 binary arrays with no 2 X 2 subblock having exactly 2 ones.

%H R. H. Hardin, <a href="/A183778/b183778.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (4,94,-260,-3104,6922,48854, -94118,-411428,687376, 1991983,-2792826,-5747356, 6404184,9882208,-8117120, -9774592,5218304,5062656, -1310720,-1048576).

%F Empirical: a(n)=4*a(n-1)+94*a(n-2)-260*a(n-3)-3104*a(n-4)+6922*a(n-5)+48854*a(n-6)-94118*a(n-7)-411428*a(n-8)+687376*a(n-9)+1991983*a(n-10)-2792826*a(n-11)-5747356*a(n-12)+6404184*a(n-13)+9882208*a(n-14)-8117120*a(n-15)-9774592*a(n-16)+5218304*a(n-17)+5062656*a(n-18)-1310720*a(n-19)-1048576*a(n-20).

%F The above recurrence is correct. See A183782 for bounds on the order of the recurrence. - _Andrew Howroyd_, Jan 09 2025

%e Some solutions with a(1,1)=0 for 3X6

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

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

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

%Y Column k=5 of A183782.

%K nonn,easy

%O 0,1

%A _R. H. Hardin_, Jan 07 2011

%E a(0) prepended by _Andrew Howroyd_, Jan 09 2025