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A200185
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Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two consecutive declines, no adjacent equal elements, and no element more than one greater than the previous (random base sawtooth pattern).
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1
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10, 29, 78, 100, 186, 246, 380, 464, 686, 798, 1096, 1276, 1658, 1878, 2408, 2668, 3306, 3672, 4432, 4852, 5814, 6288, 7398, 8010, 9278, 9960, 11486, 12236, 13944, 14870, 16774, 17780, 19998, 21088, 23528, 24826, 27494, 28890, 31930, 33424, 36720, 38456
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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) = -a(n-1) +a(n-3) +2*a(n-4) +2*a(n-5) +2*a(n-6) -2*a(n-8) -3*a(n-9) -3*a(n-10) -2*a(n-11) +2*a(n-13) +2*a(n-14) +2*a(n-15) +a(n-16) -a(n-18) -a(n-19) for n>21.
Empirical g.f.: x*(10 + 39*x + 107*x^2 + 168*x^3 + 237*x^4 + 276*x^5 + 292*x^6 + 244*x^7 + 196*x^8 + 128*x^9 + 79*x^10 + 47*x^11 + 40*x^12 + 30*x^13 + 28*x^14 + 22*x^15 + 8*x^16 - 5*x^17 - 12*x^18 - 9*x^19 - x^20) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 20 2018
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EXAMPLE
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Some solutions for n=6:
..0....3....1....3....6....2....1....2....4....3...-1....3....1....4....4....3
..1....4....2....2...-1....3...-1....3....0....4....0....0...-2....5....5....2
..2....3....0....3....0....4....0...-1....1....5...-1....1...-1...-2....1....3
..3....4....1...-3....1....5....1....0....2...-4....0...-2....0...-1....2...-2
.-2...-5...-1...-2...-1...-5....2...-1...-2...-3....1...-1....1...-3...-5...-1
.-1...-4....0...-1....0...-4...-2....0...-1...-2....0....0....2...-2...-4....0
.-3...-5...-3...-2...-5...-5...-1...-3...-4...-3....1...-1...-1...-1...-3...-5
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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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