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A205338
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Number of length n+1 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than 5.
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1
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0, 5, 20, 160, 1130, 8927, 71630, 594405, 5025740, 43243674, 377127756, 3327001441, 29634744950, 266164547110, 2407763862342, 21918167505714, 200631620380132, 1845576127894008, 17052050519557200, 158176470846492722
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OFFSET
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1,2
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COMMENTS
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Column 5 of A205341.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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a(n) = Sum_{i=1..n}((Sum_{l=0..i}(binomial(i,l)*(Sum_{j=0..(5*(i-l))/11}((-1)^j*binomial(i-l,j)*binomial(-l+5*(-l-2*j+i)-j+i-1,5*(-l-2*j+i)-j)))*(-1)^l))*a(n-i))/n, a(0)=1. - Vladimir Kruchinin, Apr 07 2017
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EXAMPLE
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Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..5....5....5....2....5....5....4....2....3....2....2....2....4....1....3....1
..8....6...10....3....8....4....6....1....5....5....6....5....7....4....1....4
..3....9....9....0....5....0....2....5....0....4....1....3....4....5....2....7
..1....4....5....3....2....2....3....2....1....3....4....4....2....3....1....3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
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PROG
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(Maxima)
a(n):=if n=0 then 1 else sum((sum(binomial(i, l)*(sum((-1)^j*binomial(i-l, j)*binomial(-l+5*(-l-2*j+i)-j+i-1, 5*(-l-2*j+i)-j), j, 0, (5*(i-l))/11))*(-1)^l, l, 0, i))*a(n-i), i, 1, n)/n; /* Vladimir Kruchinin, Apr 07 2017 */
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CROSSREFS
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Sequence in context: A133667 A354848 A318433 * A197857 A197741 A189317
Adjacent sequences: A205335 A205336 A205337 * A205339 A205340 A205341
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Jan 26 2012
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STATUS
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approved
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