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A220534
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Equals one maps: number of nX3 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal, diagonal and antidiagonal neighbors in a random 0..1 nX3 array
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1
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4, 5, 55, 322, 1802, 9888, 54152, 296677, 1626316, 8921034, 48940217, 268458544, 1472546593, 8077208658, 44305328871, 243025038817, 1333048565463, 7312079889715, 40108451658226, 220004139643941, 1206773599084364
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 5*a(n-1) +a(n-2) +5*a(n-3) +33*a(n-4) -53*a(n-5) +9*a(n-6) -86*a(n-7) -255*a(n-8) -958*a(n-9) -2148*a(n-10) +2*a(n-11) +3703*a(n-12) +3911*a(n-13) +2790*a(n-14) +6350*a(n-15) +25490*a(n-16) +33796*a(n-17) +20951*a(n-18) +17342*a(n-19) +22582*a(n-20) +18944*a(n-21) -21214*a(n-22) -38176*a(n-23) -7890*a(n-24) +49122*a(n-25) +10920*a(n-26) -56928*a(n-27) -35976*a(n-28) +34352*a(n-29) +127432*a(n-30) +82976*a(n-31) -13984*a(n-32) -42432*a(n-33) -36448*a(n-34) +9952*a(n-35) +24384*a(n-36) -1664*a(n-38) +3072*a(n-39) +1152*a(n-40) for n>42
Empirical G.f.: -3*x^2 + 2*x + (-32071680*x^39 - 100122624*x^38 - 24109056*x^37 + 194641920*x^36 + 168394752*x^35 - 220428288*x^34 - 431751168*x^33 + 159621120*x^32 + 1002580992*x^31 + 697549824*x^30 - 440838144*x^29 - 1008253440*x^28 - 720403200*x^27 + 73875456*x^26 + 471329280*x^25 + 352829952*x^24 + 292103424*x^23 + 261794304*x^22 + 177937920*x^21 + 46722816*x^20 - 15743232*x^19 - 45053568*x^18 - 16857216*x^17 - 54782208*x^16 - 47704320*x^15 - 6238080*x^14 - 1480320*x^13 + 8354304*x^12 + 517248*x^11 + 445824*x^10 + 3734784*x^9 + 870912*x^8 - 19584*x^7 - 383616*x^6 - 351360*x^5 + 51840*x^4 - 21888*x^3 + 11520*x^2 + 16128*x - 4608)/(3456*(1152*x^40 + 3072*x^39 - 1664*x^38 + 24384*x^36 + 9952*x^35 - 36448*x^34 - 42432*x^33 - 13984*x^32 + 82976*x^31 + 127432*x^30 + 34352*x^29 - 35976*x^28 - 56928*x^27 + 10920*x^26 + 49122*x^25 - 7890*x^24 - 38176*x^23 - 21214*x^22 + 18944*x^21 + 22582*x^20 + 17342*x^19 + 20951*x^18 + 33796*x^17 + 25490*x^16 + 6350*x^15 + 2790*x^14 + 3911*x^13 + 3703*x^12 + 2*x^11 - 2148*x^10 - 958*x^9 - 255*x^8 - 86*x^7 + 9*x^6 - 53*x^5 + 33*x^4 + 5*x^3 + x^2 + 5*x - 1)). - Vaclav Kotesovec, Dec 16 2012
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EXAMPLE
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Some solutions for n=3
..1..0..1....1..1..1....1..1..1....1..0..1....1..0..1....0..1..0....0..1..0
..1..1..0....0..0..0....1..0..0....1..0..1....0..0..1....0..1..0....1..0..0
..0..1..0....0..0..0....1..0..1....0..0..0....0..0..0....0..1..0....1..0..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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