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Search: id:A027582
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| A027582 |
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Sequence satisfies T(T(a))=a, where T is defined below. |
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+0
2
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| 1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 17, 20, 21, 25, 29, 31, 35, 39, 43, 48, 53, 57, 62, 70, 75, 82, 90, 96, 106, 116, 124, 135, 146, 157, 170, 184, 197, 211, 229, 244, 262, 282, 300, 322, 346, 368, 393, 420, 447, 476, 508, 539, 572, 611, 646, 685
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, Nov 15 1996.
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LINKS
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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.
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FORMULA
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Define T:a->b by: given a0<=a1<=..., remove duplicates, keep only odd numbers, getting c0<c1<...; define b0, b1, b2, ... by Sum bi*x^i = Product 1/(1-x^ci). - Description corrected by and more terms from Michael Somos, May 04 2003.
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EXAMPLE
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1 + 1x + 1x^2 + 2x^3 + 2x^4 + 3x^5 + 4x^6 + 5x^7 + 6*x^8 + 8*x^9 + 10*x^10 + 12*x^11 + 15*x^12 + ... = 1/((1 - x^1)(1 - x^3)(1 - x^5)(1 - x^7)(1 - x^9)(1 - x^11)(1 - x^15)(1 - x^17)(1 - x^21)...)
1 + 1x + 1x^2 + 2x^3 + 2x^4 + 3x^5 + 4x^6 + 4x^7 + 5*x^8 + 6*x^9 + 7*x^10 + 8*x^11 + 9*x^12 + ... = 1/((1 - x^1)(1 - x^3)(1 - x^5)(1 - x^15)(1 - x^17)(1 - x^21)...)
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CROSSREFS
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Cf. A027581=T(a).
Sequence in context: A011885 A008672 A097923 this_sequence A011880 A029044 A029043
Adjacent sequences: A027579 A027580 A027581 this_sequence A027583 A027584 A027585
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KEYWORD
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nonn,easy,eigen
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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