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Search: id:A117684
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| A117684 |
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Sum of the rows of Compositnomial function: a triangular binomial like function made up of a product of only composite numbers. |
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1
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| 1, 2, 3, 13, 11, 49, 27, 141, 523, 3081, 923, 5509, 1371, 7617, 24391, 84933, 14795, 110329, 20859, 142101, 499843, 1858209, 241211, 2312077, 8417451
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In contrast to Pascal's triangle these sums alternate in Magnitude.
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FORMULA
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f[n]= 1 if n is prime and n otherwise cf[0]=1; cf(n) = f[n]*a[n-1] bf[n,m]=cf[n]/(cf[m]*cf[n - m]) a[n]=Sum[bf[n,m],{m,1,n}]
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EXAMPLE
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1
1, 1
1, 1, 1
4, 4, 4, 1
1, 4, 4, 1, 1,
6, 6, 24, 6, 6, 1
1, 6, 6, 6, 6, 1, 1
8, 8, 48, 12, 48, 8, 8, 1
9, 72, 72, 108, 108, 72, 72, 9, 1
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MATHEMATICA
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cf[0] = 1; cf[n_Integer?Positive] := cf[n] = f[n]*cf[n - 1] bf[n_Integer?Positive, m_Integer?Positive] := bf[n, m] = cf[n]/(cf[m]*cf[n - m]) b = Table[Table[bf[n, m], {m, 1, n}], {n, 1, 10}] MatrixForm[b] Flatten[b] c = Table[Apply[Plus, Table[bf[n, m], {m, 1, n}]], {n, 1, 25}] ListPlot[c, PlotJoined -> True]
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CROSSREFS
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Sequence in context: A074478 A132365 A129671 this_sequence A056445 A100385 A128460
Adjacent sequences: A117681 A117682 A117683 this_sequence A117685 A117686 A117687
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 12 2006
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