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A186933 Number of (n+1) X 4 binary arrays with every 2 X 2 subblock trace equal to exactly one or two horizontal and vertical neighbor 2 X 2 subblock traces. 1

%I #7 Nov 30 2012 21:47:07

%S 40,472,1840,10496,46960,241320,1152312,5769904,28108104,138858120,

%T 680168896,3348217496,16439521504,80842220784,397185103728,

%U 1952368430392,9594044732176,47153665649656,231733527347608,1138902729415320

%N Number of (n+1) X 4 binary arrays with every 2 X 2 subblock trace equal to exactly one or two horizontal and vertical neighbor 2 X 2 subblock traces.

%C Column 3 of A186939.

%H R. H. Hardin, <a href="/A186933/b186933.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n)=2*a(n-1)+7*a(n-2)+5*a(n-3)+96*a(n-4)+211*a(n-5)+224*a(n-6) +359*a(n-7)+2432*a(n-8)-5349*a(n-9)-17935*a(n-10)+3082*a(n-11) +13564*a(n-12) -15993*a(n-13)-84187*a(n-14)+92372*a(n-15)+127000*a(n-16) -113898*a(n-17)+144310*a(n-18)+918134*a(n-19)-1086743*a(n-20) +1853525*a(n-21)-2311497*a(n-22)+3080068*a(n-23)-2708002*a(n-24) +3885818*a(n-25)+2851259*a(n-26)-17123197*a(n-27)+26222153*a(n-28) -9952550*a(n-29)-15769993*a(n-30)+24911652*a(n-31)-10552895*a(n-32) -6025188*a(n-33)+13047010*a(n-34)-9024341*a(n-35)-3552852*a(n-36) +13989635*a(n-37)-9282924*a(n-38)-4282939*a(n-39)+7214307*a(n-40) -1284491*a(n-41)-1670630*a(n-42)-301130*a(n-43)+1276294*a(n-44) -464696*a(n-45)-615900*a(n-46)+484152*a(n-47)+864*a(n-48)-77312*a(n-49) +26624*a(n-50) for n>53.

%e Some solutions for 6 X 4:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2011

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Last modified February 23 17:43 EST 2024. Contains 370283 sequences. (Running on oeis4.)