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.

40, 472, 1840, 10496, 46960, 241320, 1152312, 5769904, 28108104, 138858120, 680168896, 3348217496, 16439521504, 80842220784, 397185103728, 1952368430392, 9594044732176, 47153665649656, 231733527347608, 1138902729415320

Offset

1,1

Comments

Column 3 of A186939.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

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.

Example

Some solutions for 6 X 4:
..1..0..0..0....0..1..0..0....1..1..0..0....1..1..1..1....0..0..0..1
..1..0..0..1....0..1..0..0....1..1..1..1....0..1..1..0....0..0..0..0
..1..0..0..1....0..1..1..0....1..0..0..0....0..0..1..0....0..1..1..1
..0..0..0..0....1..1..1..0....1..0..0..0....1..0..0..0....0..0..1..1
..1..1..1..0....1..0..1..0....0..0..1..1....0..0..0..0....1..0..0..0
..1..1..1..1....0..0..1..0....1..0..0..0....0..1..1..0....1..0..1..1

Crossrefs

Sequence in context: A055750 A290611 A115189 * A271650 A177096 A202902

Adjacent sequences: A186930 A186931 A186932 * A186934 A186935 A186936

Keyword

nonn

Author

R. H. Hardin, Mar 01 2011

Status

approved