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Search: id:A116578
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| A116578 |
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Integerization of a truncated Pascal root structure with a power of two level pumping. |
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+0
1
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| 2, 0, 4, 4, 4, 8, 0, 11, 11, 16, 9, 9, 25, 25, 32, 0, 31, 31, 55, 55, 64, 28, 28, 79, 79, 115, 115, 128, 0, 97, 97, 181, 181, 236, 236, 255, 88, 88, 256, 256, 392, 392, 481, 481, 512, 0, 316, 316, 601, 601, 828, 828, 973, 973, 1024
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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I used a backward representation of the roots so that the least comes first: the results behaves like an ecomomics or population curve. When taken as Modulo two one ca see a pattern like that of Pascal's triangle in the zeros and ones. The alternating (t-1)^n polynomials are solved as: (t-1)^n=1 and instead of the 2^n coeffiecents, the roots are used for sequence. It is a unique new approach to the problrem of Pascal's triangle.
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FORMULA
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a(n) = Table[Table[Floor[2^(n - 1)*Abs[x]] /. NSolve[(x - 1)^n - 1 == 0.x][[m]], {m, n, 1, -1}], {n, 1, 10}]
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EXAMPLE
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Triangular form of the sequence:
{2}
{0, 4}
{4, 4, 8}
{0, 11, 11, 16}
{9, 9, 25, 25, 32}
{0, 31, 31, 55, 55, 64}
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MATHEMATICA
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Table[Table[Floor[2^(n - 1)*Abs[x]] /. NSolve[(x - 1)^n - 1 == 0.x][[m]], {m, n, 1, -1}], {n, 1, 10}] Flatten[a]
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CROSSREFS
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Adjacent sequences: A116575 A116576 A116577 this_sequence A116579 A116580 A116581
Sequence in context: A114122 A004174 A049797 this_sequence A078050 A134271 A094403
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KEYWORD
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nonn,uned,probation,obsc
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AUTHOR
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Roger L Bagula (rlbagulatftn(AT)yahoo.com), Mar 21 2006
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