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A162849
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Pairs of numbers n that add up to the 'backward decimal expansion' of fraction 1/109 and whose difference is the 'backward decimal expansion' of fraction 1/89
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5
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0, 1, 10, 101, 2010, 10201, 303010, 1040201, 40703010, 107050201, 5140803010, 11112050201, 625200803010, 1162613050201, 74146210803010, 122513313050201, 8639754210803010, 12992793413050201, 993903355210803010
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Sum of pairs also (consecutive) cumulative sum of 110^n (or numerators of 1/110^1 + 1/110^2 + ...1/110^n, representing fraction 1/109).
Difference of pairs also cumulative sum of 90^n (or numerators of 1/90^1 + 1/90^2 +...1/90^n, representing fraction 1/89).
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FORMULA
| For n even: a(n)=100*a(n-2)+10*a(n-1),for n odd: a(n)=100*a(n-2)+10*a(n-3)+1; with a(0)=0,a(1)=1
a(n)= 201*a(n-2) -10100*a(n-4) +9900*a(n-6). G.f.: x^2*(-1-10*x+100*x^2)/((x-1)*(1+x)*(90*x^2-1)*(110*x^2-1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 11 2010]
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EXAMPLE
| In pairs:
0,1
10,101
2010,10201
303010,1040201
40703010,107050201
5140803010,11112050201
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CROSSREFS
| Cf. A162741, A161999, A007318, A000045
Sequence in context: A163461 A081192 A108892 * A041182 A061107 A036299
Adjacent sequences: A162846 A162847 A162848 * A162850 A162851 A162852
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KEYWORD
| nonn,base,less
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AUTHOR
| Mark Dols (markdols99(AT)yahoo.com), Jul 14 2009
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 11 2010
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