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A247721
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Number of length n+3 0..3 arrays with no disjoint pairs in any consecutive four terms having the same sum
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1
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168, 456, 1248, 3424, 9392, 25822, 71060, 195536, 537880, 1480026, 4073228, 11209522, 30845400, 84880220, 233584180, 642804172, 1768901108, 4867756146, 13395492168, 36862857286, 101441854028, 279154735896, 768198993968
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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) = 2*a(n-1) -3*a(n-2) +8*a(n-3) +16*a(n-4) -8*a(n-5) +46*a(n-6) -48*a(n-7) -25*a(n-8) -38*a(n-10) +62*a(n-11) -58*a(n-12) +72*a(n-13) -354*a(n-14) +246*a(n-15) -26*a(n-16) +162*a(n-17) -183*a(n-18) -112*a(n-19) -34*a(n-20) +112*a(n-21) +320*a(n-22) -166*a(n-23) -80*a(n-24) -90*a(n-25) -12*a(n-26) +72*a(n-27).
Empirical g.f.: -2*x*(84 +60*x +420*x^2 +687*x^5 -784*x^12 +7433*x^21 -1924*x^6 -983*x^7+2304*x^26 -394*x^8 +564*x^25 +6460*x^20 -6844*x^22 -2604*x^24 -911*x^9 -3644*x^23 -24*x^15+1603*x^19 -2826*x^18 -2238*x^11 -6952*x^17 -24*x^4 +1024*x^10 -8176*x^13 +7852*x^14 +476*x^3 +2294*x^16) / ( -1 +2*x -3*x^2 -8*x^5 -58*x^12 +112*x^21 +46*x^6 -48*x^7 -12*x^26 -25*x^8 -90*x^25 -34*x^20 +320*x^22 -80*x^24 -166*x^23 +246*x^15 -112*x^19 -183*x^18 +62*x^11 +162*x^17 +16*x^4 -38*x^10 +72*x^27 +72*x^13 -354*x^14 +8*x^3 -26*x^16 ). - R. J. Mathar, Sep 23 2014
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EXAMPLE
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Some solutions for n=6
..0....0....3....3....1....2....1....0....2....1....1....2....2....1....3....3
..1....0....2....3....2....3....3....2....1....1....1....2....3....3....3....0
..0....2....0....0....0....1....1....0....3....3....0....3....3....1....1....2
..3....3....3....2....2....1....2....0....3....2....3....0....1....0....0....0
..3....0....2....2....3....1....3....0....0....3....3....2....3....1....0....0
..3....2....3....3....0....0....1....1....3....1....3....2....0....3....2....0
..0....0....0....0....3....1....3....2....3....3....1....1....1....0....0....2
..3....0....3....0....1....3....0....2....2....0....3....0....0....0....0....1
..3....1....3....2....0....1....3....0....1....1....3....0....2....0....0....0
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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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