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Search: id:A123638
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| A123638 |
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Consider the 2^n compositions of n and count only those ending in an odd part with row sum A001045. |
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+0
4
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| 1, 1, 3, 8, 25, 83, 299, 1158, 4813, 21373, 100955, 504916, 2662761, 14754311, 85643459, 519493938, 3285790317, 21628225041, 147887079907, 1048634836288, 7698589399833, 58432476430139, 457901993065915, 3700291495531166
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OFFSET
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1,3
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COMMENT
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Compositions ending in an even part yield sequence 0 1 2 6 18 ... A123639. and a(n)+A123639(n) = A047970(n). Ending parity of compositions can be detected using mod(A065120,2)
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EXAMPLE
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4
31 32 33
211 221 222
1111
Consider the above multisets: permute and note the parity of the ending part of each of the 14 compositions.
4
31 13 32 23 33
211 121 112 221 212 122 222
1111
4 is even
31 13 23 and 33 are odd
32 is even
etc
there are 0 + 4 + 3 + 1 = 8 odd compositions therefore a(4)=8.
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MAPLE
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g:= proc(b, t, l, m) option remember; if t=0 then b*l else add (g(b, t-1, irem(k, 2), m), k=1..m-1) +g(1, t-1, irem(m, 2), m) fi end: a:= n-> add (g(0, k, 0, n+1-k), k=1..n): seq (a(n), n=1..30);
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CROSSREFS
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Cf. A001045 A047970 A065120 A123639 A123640 A123641.
Sequence in context: A148795 A148796 A148797 this_sequence A038665 A006372 A151426
Adjacent sequences: A123635 A123636 A123637 this_sequence A123639 A123640 A123641
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KEYWORD
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nonn
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), Oct 04 2006
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EXTENSIONS
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Offset corrected, Maple program and more terms by Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 06 2009
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