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Search: id:A140895
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| A140895 |
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A Lucas-Binet triangle read by rows: t(n,m)=((( 1 + Sqrt[Prime[n]]))^m + (( 1 - Sqrt[Prime[n]]))^m)/2. |
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1
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| 1, 1, 4, 1, 6, 16, 1, 8, 22, 92, 1, 12, 34, 188, 716, 1, 14, 40, 248, 976, 4928, 1, 18, 52, 392, 1616, 9504, 44864, 1, 20, 58, 476, 1996, 12560, 61048, 348176, 1, 24, 70, 668, 2876, 20448, 104168, 658192, 3608080, 1, 30, 88, 1016, 4496, 37440, 200768
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are: {1, 5, 23, 123, 951, 6207, 56447, 424335, 4394527, 67853311, ...}.
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REFERENCES
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Arthur Benjamin and Jennifer J. Quinn, Fibonacci and Lucas Identities through Colored Tilings, Utilitas Mathematica, Vol 56, pp. 137-142, November, 1999. http://www.math.hmc.edu/~benjamin/papers.html
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FORMULA
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t(n,m)=((( 1 + Sqrt[Prime[n]]))^m + (( 1 - Sqrt[Prime[n]]))^m)/2.
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EXAMPLE
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{1},
{1, 4},
{1, 6, 16},
{1, 8, 22, 92},
{1, 12, 34, 188, 716},
{1, 14, 40, 248, 976, 4928},
{1, 18, 52, 392, 1616, 9504, 44864},
{1, 20, 58, 476, 1996, 12560, 61048, 348176},
{1, 24, 70, 668, 2876, 20448, 104168, 658192, 3608080},
{1, 30, 88, 1016, 4496, 37440, 200768, 1449856, 8521216, 57638400}
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MATHEMATICA
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Binet[n_, m_] = ((( 1 + Sqrt[Prime[n]]))^m + (( 1 - Sqrt[Prime[n]]))^m)/2; a = Table[Table[ExpandAll[Binet[n, m]], {m, 1, n}], {n, 1, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A083843 A094264 A056140 this_sequence A126150 A096966 A140703
Adjacent sequences: A140892 A140893 A140894 this_sequence A140896 A140897 A140898
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 23 2008
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 01 2008
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