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Number of (n+2)X6 binary arrays with no more than one of any consecutive three bits set in any row or column
1

%I #5 Mar 31 2012 12:36:47

%S 739,5167,37029,259651,1823347,12853815,90488829,636713695,4482191171,

%T 31552566393,222091707777,1563301187969,11004262988247,77459398723649,

%U 545238701722185,3837961695887271,27015585227632543,190163795686945801

%N Number of (n+2)X6 binary arrays with no more than one of any consecutive three bits set in any row or column

%C Column 4 of A202421

%H R. H. Hardin, <a href="/A202417/b202417.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +15*a(n-2) +163*a(n-3) +435*a(n-4) -312*a(n-5) -6058*a(n-6) -20551*a(n-7) -10846*a(n-8) +129529*a(n-9) +382414*a(n-10) +214587*a(n-11) -1252567*a(n-12) -3718269*a(n-13) -2774661*a(n-14) +7541788*a(n-15) +20442871*a(n-16) +15190133*a(n-17) -16329959*a(n-18) -59139819*a(n-19) -73602496*a(n-20) -10192761*a(n-21) +98952469*a(n-22) +167803153*a(n-23) +149515753*a(n-24) -7453678*a(n-25) -215498436*a(n-26) -282603533*a(n-27) -222705450*a(n-28) -24104176*a(n-29) +248207971*a(n-30) +302814223*a(n-31) +242555242*a(n-32) +89632215*a(n-33) -138303598*a(n-34) -194727635*a(n-35) -160749598*a(n-36) -108454542*a(n-37) +27857814*a(n-38) +55543779*a(n-39) +55776272*a(n-40) +56989956*a(n-41) -63166*a(n-42) +4750982*a(n-43) -12142956*a(n-44) -8474055*a(n-45) -1877613*a(n-46) -2528704*a(n-47) +1168456*a(n-48) +249876*a(n-49) +279332*a(n-50) +195827*a(n-51) -50365*a(n-52) +16393*a(n-53) -15338*a(n-54) -3822*a(n-55) +812*a(n-56) -678*a(n-57) +307*a(n-58) +2*a(n-59) -2*a(n-60) +4*a(n-61) -a(n-62)

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 19 2011