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A228464
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Number of arrays of maxima of three adjacent elements of some 0..n array of length 9.
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2
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44, 383, 1821, 6254, 17487, 42386, 92430, 185727, 349558, 623513, 1063283, 1745172, 2771393, 4276212, 6433004, 9462285, 13640784, 19311619, 26895641, 36904010, 49952067, 66774566, 88242330, 115380395, 149387706, 191658429, 243804943
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OFFSET
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1,1
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COMMENTS
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See A228461 for explanation of definition.
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LINKS
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FORMULA
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Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (91/45)*n^5 + (63/8)*n^4 + (2557/180)*n^3 + (517/40)*n^2 + (2419/420)*n + 1 = (n+1) *(n+2) *(32*n^5 + 408*n^4 + 3808*n^3 + 7605*n^2 + 5367*n + 1260)/2520.
G.f.: x*(44 + 31*x - 11*x^2 - 54*x^3 + 75*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
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EXAMPLE
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Some solutions for n=4:
3 0 3 4 4 3 3 4 3 4 2 3 2 0 3 2
3 0 2 4 4 0 0 2 1 3 4 3 0 0 4 0
0 0 2 4 0 2 0 2 4 4 4 3 4 0 4 2
0 0 1 3 1 3 1 2 4 4 4 3 4 4 4 2
0 0 3 1 1 3 2 2 4 4 0 1 4 4 0 2
1 0 3 0 4 4 3 2 4 4 0 1 0 4 3 2
1 3 4 3 4 4 3 1 0 2 1 2 0 3 3 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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