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A034297
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Number of ordered positive integer solutions (m_1, m_2, ..., m_k) (for some k) to Sum_{i=1..k} m_i=n with |m_i-m_{i-1}| <= 1 for i = 2 ... k.
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6
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1, 2, 4, 6, 11, 17, 29, 47, 78, 130, 215, 357, 595, 990, 1651, 2748, 4584, 7643, 12744, 21256, 35451, 59133, 98636, 164531, 274463, 457837, 763746, 1274060, 2125356, 3545491, 5914545, 9866602, 16459421, 27457549, 45804648, 76411272, 127469285, 212644336
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OFFSET
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1,2
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COMMENTS
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Compositions of n where successive parts differ by at most 1, see example. [Joerg Arndt, Dec 10 2012]
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..1000
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EXAMPLE
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From Joerg Arndt, Dec 10 2012: (Start)
The a(6) = 17 such compositions of 6 are
[ #] composition
[ 1] [ 1 1 1 1 1 1 ]
[ 2] [ 1 1 1 1 2 ]
[ 3] [ 1 1 1 2 1 ]
[ 4] [ 1 1 2 1 1 ]
[ 5] [ 1 1 2 2 ]
[ 6] [ 1 2 1 1 1 ]
[ 7] [ 1 2 1 2 ]
[ 8] [ 1 2 2 1 ]
[ 9] [ 1 2 3 ]
[10] [ 2 1 1 1 1 ]
[11] [ 2 1 1 2 ]
[12] [ 2 1 2 1 ]
[13] [ 2 2 1 1 ]
[14] [ 2 2 2 ]
[15] [ 3 2 1 ]
[16] [ 3 3 ]
[17] [ 6 ]
(End)
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MAPLE
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b:= proc(n, i) option remember;
`if`(n=i, 1, `if`(n<0 or i<1, 0, add(b(n-i, i+j), j=-1..1)))
end:
a:= n-> add(b(n, k), k=1..n):
seq (a(n), n=1..50); # Alois P. Heinz, Jul 06 2012
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PROG
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(PARI) T = matrix(70, 70, i, j, -1); doIt(last, left) = local(c); c = T[last, left]; if (c == -1, c = 0; for (i = max(1, last - 1), last + 1, c += b(i, left - i)); T[last, left] = c); c; b(last, left) = if (left == 0, return(1)); if (left < 0, return(0)); doIt(last, left); a(n) = sum (i = 1, n, b(i, n - i)); (Wasserman)
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CROSSREFS
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Cf. A003116, A034296.
Column k=1 of A214246, A214248.
Sequence in context: A115315 A004698 A014217 * A026636 A026658 A138688
Adjacent sequences: A034294 A034295 A034296 * A034298 A034299 A034300
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KEYWORD
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nonn
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AUTHOR
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Erich Friedman
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EXTENSIONS
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More terms from David Wasserman, Feb 02 2006
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STATUS
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approved
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