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A250383
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Number of length n+3 0..4 arrays with no four consecutive terms having the maximum of any two terms equal to the minimum of the remaining two terms.
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1
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420, 1560, 5848, 21950, 82398, 309452, 1162292, 4365720, 16398414, 61595866, 231368150, 869073568, 3264448894, 12262057782, 46059259710, 173009763590, 649866719912, 2441057378296, 9169205035462, 34441763801094, 129371640763978
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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) +7*a(n-2) -7*a(n-3) +31*a(n-4) +27*a(n-5) -237*a(n-6) -42*a(n-7) +109*a(n-8) -809*a(n-9) +976*a(n-10) +2527*a(n-11) -1891*a(n-12) -83*a(n-13) +2938*a(n-14) -3839*a(n-15) -1155*a(n-16) +1894*a(n-17) -2913*a(n-18) +471*a(n-19) +2319*a(n-20) -198*a(n-21) +36*a(n-22) -216*a(n-24).
Empirical g.f.: 2*x*(210 + 360*x - 106*x^2 + 1137*x^3 - 2269*x^4 - 13879*x^5 - 1808*x^6 + 386*x^7 - 22089*x^8 + 87395*x^9 + 113109*x^10 - 104339*x^11 + 25652*x^12 + 99193*x^13 - 238490*x^14 - 38645*x^15 + 71125*x^16 - 154383*x^17 + 67320*x^18 + 134124*x^19 - 12168*x^20 + 864*x^21 - 3888*x^22 - 12960*x^23) / (1 - 2*x - 7*x^2 + 7*x^3 - 31*x^4 - 27*x^5 + 237*x^6 + 42*x^7 - 109*x^8 + 809*x^9 - 976*x^10 - 2527*x^11 + 1891*x^12 + 83*x^13 - 2938*x^14 + 3839*x^15 + 1155*x^16 - 1894*x^17 + 2913*x^18 - 471*x^19 - 2319*x^20 + 198*x^21 - 36*x^22 + 216*x^24). - Colin Barker, Aug 20 2017
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EXAMPLE
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Some solutions for n=5:
..2....4....3....4....2....4....3....0....4....4....4....0....1....0....0....4
..3....0....1....3....4....4....2....1....0....1....1....2....4....4....2....3
..4....3....0....1....3....2....1....0....4....4....4....3....0....2....4....4
..4....1....3....4....2....3....4....3....2....2....0....1....2....4....1....2
..0....4....0....1....0....1....0....3....3....0....3....3....0....1....3....0
..1....1....2....2....0....4....3....0....0....4....4....2....4....0....0....3
..2....2....3....0....2....0....2....0....0....4....4....4....0....3....3....1
..4....0....3....0....3....4....4....4....3....2....0....2....1....2....2....2
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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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