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A090752
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Number of compositions (ordered partitions) of n whereby at most 1 increase is allowed and this increase must be by 1.
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0
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1, 2, 4, 7, 13, 21, 36, 56, 89, 134, 204, 296, 435, 618, 879, 1223, 1702, 2323, 3171, 4263, 5720, 7589, 10043, 13158, 17202, 22305, 28839, 37038, 47437, 60391, 76686, 96872, 122047, 153081, 191513, 238625, 296620, 367379, 453948, 559112, 687107
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OFFSET
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1,2
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COMMENTS
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Number of compositions of n in which exactly 1 increase is allowed and this increase must be by 1, is a(n)-A000041(n). - Vladeta Jovovic, Feb 09 2004
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LINKS
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Table of n, a(n) for n=1..41.
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EXAMPLE
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a(5)=13, as we have 5, 41, 32, 23, 311, 221, 212, 122, 2111, 1211, 1121, 1112 and 11111.
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PROG
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(PARI) Ta = matrix(70, 70, i, j, -1); Tn = Ta; doAllowed(last, left) = local(c); c = Ta[last, left]; if (c == -1, c = 0; for (i = 1, min(last, left), c += b(i, left - i, 1)); c += b(last + 1, left - last - 1, 0); Ta[last, left] = c); c; doNot(last, left) = local(c); c = Tn[last, left]; if (c == -1, c = 0; for (i = 1, min(last, left), c += b(i, left - i, 0)); Tn[last, left] = c); c; b(last, left, allowed) = if (left == 0, return(1)); if (left < 0, return(0)); if (allowed, doAllowed(last, left), doNot(last, left)); a(n) = sum (i = 1, n, b(i, n - i, 1)); (Wasserman)
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CROSSREFS
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Cf. A034297, A003116.
Sequence in context: A037032 A165753 A205183 * A051058 A026625 A026691
Adjacent sequences: A090749 A090750 A090751 * A090753 A090754 A090755
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KEYWORD
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nonn,changed
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AUTHOR
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Jon Perry, Feb 06 2004
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EXTENSIONS
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More terms from Vladeta Jovovic, Feb 13 2004
More terms from David Wasserman, Feb 02 2006
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STATUS
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approved
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