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Search: id:A117145
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| A117145 |
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Triangle read by rows: T(n,k) is the number of partitions of n into parts of the form 2^j-1, j=1,2,... and having k parts (n>=1, k>=1). Partitions into parts of the form 2^j-1, j=1,2,... are called s-partitions. |
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+0
3
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| 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1
(list; table; graph; listen)
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OFFSET
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1,39
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COMMENT
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Row sums yield A000929. sum(k*T(n,k),k=1..n)=A117146(n).
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REFERENCES
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P. C. P. Bhatt, An interesting way to partition a number, Inform. Process. Lett., 71, 1999, 141-148.
W. M. Y. Goh, P. Hitczenko, A. Shokoufandeh, s-partitions, Inform. Process. Lett., 82, 2002, 327-329.
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FORMULA
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G.f.=G(t,x)=-1+1/product(1-tx^(2^k-1), k=1..infinity).
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EXAMPLE
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T(9,3)=2 because we have [7,1,1] and [3,3,3].
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MAPLE
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g:=-1+1/product(1-t*x^(2^k-1), k=1..10): gser:=simplify(series(g, x=0, 20)): for n from 1 to 19 do P[n]:=sort(coeff(gser, x^n)) od: for n from 1 to 19 do seq(coeff(P[n], t^j), j=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000929, A117146.
Sequence in context: A123671 A090418 A085854 this_sequence A083912 A104975 A106404
Adjacent sequences: A117142 A117143 A117144 this_sequence A117146 A117147 A117148
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 2006
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