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A251429
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Number of length 2+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.
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1
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12, 41, 116, 237, 432, 725, 1128, 1641, 2316, 3145, 4148, 5357, 6776, 8413, 10328, 12489, 14924, 17689, 20764, 24149, 27928, 32061, 36568, 41513, 46868, 52641, 58924, 65653, 72856, 80621, 88896, 97681, 107092, 117057, 127596, 138805, 150624, 163061
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = a(n-1) + 2*a(n-3) - a(n-4) - a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) + a(n-10) - a(n-11).
Empirical for n mod 12 = 0: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + 1
Empirical for n mod 12 = 1: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (97/54)
Empirical for n mod 12 = 2: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (43/27)
Empirical for n mod 12 = 3: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (11/2)
Empirical for n mod 12 = 4: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (35/27)
Empirical for n mod 12 = 5: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (113/54)
Empirical for n mod 12 = 6: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + 1
Empirical for n mod 12 = 7: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (313/54)
Empirical for n mod 12 = 8: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (43/27)
Empirical for n mod 12 = 9: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (3/2)
Empirical for n mod 12 = 10: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (35/27)
Empirical for n mod 12 = 11: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (329/54)
Empirical g.f.: x*(12 + 29*x + 75*x^2 + 97*x^3 + 125*x^4 + 114*x^5 + 98*x^6 + 55*x^7 + 27*x^8 + x^9 - x^10) / ((1 - x)^4*(1 + x)*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Nov 29 2018
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EXAMPLE
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Some solutions for n=10:
..1....1....5....1....6....1....1....0....5....4....8....2....7....8....0....6
..7....8...10....7....4....6....3....3....6....6....3....6....2....6....6....7
.10....3....7....3....3...10....5....1....3....7....9....5...10....6....2....1
..7....7....8....9....6....1....1....4....5....4....1....9....7....8....5....9
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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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