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Search: id:A124754
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| A124754 |
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Alternating sum of compositions in standard order. |
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+0
2
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| 0, 1, 2, 0, 3, 1, -1, 1, 4, 2, 0, 2, -2, 0, 2, 0, 5, 3, 1, 3, -1, 1, 3, 1, -3, -1, 1, -1, 3, 1, -1, 1, 6, 4, 2, 4, 0, 2, 4, 2, -2, 0, 2, 0, 4, 2, 0, 2, -4, -2, 0, -2, 2, 0, -2, 0, 4, 2, 0, 2, -2, 0, 2, 0, 7, 5, 3, 5, 1, 3, 5, 3, -1, 1, 3, 1, 5, 3, 1, 3, -3, -1, 1, -1, 3, 1, -1, 1, 5, 3, 1, 3, -1, 1, 3, 1, -5, -3, -1, -3, 1, -1, -3, -1, 3
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The standard order of compositions is given by A066099.
The sum of row n is 2^{n-1} for n>0.
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FORMULA
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For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k (-1)^{i-1} b(i).
a(2^k) = k+1. If n = 2^e_1 + 2^e_2 + k, 0 <= k < 2^e_2 < 2^e_1, then a(n) = (e_1 - e_2) - a(2^e_2 + k).
a(0) = 0; for n>0, a(n) = a(floor(n/2)) - A106400(n).
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EXAMPLE
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Composition number 11 is 2,1,1; 2-1+1 = 2, so a(11) = 2.
The table starts:
0
1
2 0
3 1 -1 1
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CROSSREFS
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Cf. A066099, A070939, A124756, A011782 (row lengths), A106400.
Sequence in context: A002187 A124756 A113504 this_sequence A047983 A070812 A061865
Adjacent sequences: A124751 A124752 A124753 this_sequence A124755 A124756 A124757
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KEYWORD
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easy,sign,tabf
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006
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