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Search: id:A105114
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| A105114 |
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Triangle read by rows: T(n,k) is the number of compositions of n having exactly k parts equal to 2. |
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+0
4
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| 1, 1, 1, 1, 2, 2, 4, 3, 1, 7, 6, 3, 12, 13, 6, 1, 21, 26, 13, 4, 37, 50, 30, 10, 1, 65, 96, 66, 24, 5, 114, 184, 139, 59, 15, 1, 200, 350, 288, 140, 40, 6, 351, 661, 591, 318, 105, 21, 1, 616, 1242, 1199, 704, 266, 62, 7, 1081, 2324, 2406, 1533, 645, 174, 28, 1, 1897, 4332
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OFFSET
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0,5
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COMMENT
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Row n has 1+floor(n/2) terms. Row sums are the powers of 2 (A000079). Column 0 yields A005251.
Number of binary words of length n-1 having k isolated 0's. Example: T(5,1)=6 because we have 0111, 0100, 1011, 1101, 0010, and 1110. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 21 2006
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FORMULA
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G.f.=(1-z)/(1-2z+z^2-z^3-tz^2+tz^3).
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EXAMPLE
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T(7,3)=4 because we have (1,2,2,2),(2,1,2,2),(2,2,1,2) and (2,2,2,1).
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MAPLE
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G:=(1-z)/(1-2*z-z^2*t+z^3*t+z^2-z^3):Gser:=simplify(series(G, z=0, 18)): P[0]:=1: for n from 1 to 16 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 16 do seq(coeff(t*P[n], t^k), k=1..1+floor(n/2)) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000079, A005251.
Sequence in context: A129243 A084896 A011388 this_sequence A098086 A045828 A058526
Adjacent sequences: A105111 A105112 A105113 this_sequence A105115 A105116 A105117
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 07 2005
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