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A062510
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a(n) = 2^n + (-1)^(n+1).
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35
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0, 3, 3, 9, 15, 33, 63, 129, 255, 513, 1023, 2049, 4095, 8193, 16383, 32769, 65535, 131073, 262143, 524289, 1048575, 2097153, 4194303, 8388609, 16777215, 33554433, 67108863, 134217729, 268435455, 536870913, 1073741823, 2147483649
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OFFSET
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0,2
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COMMENTS
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The identity 2 = 2^2/3 + 2^3/(3*3) - 2^4/(3*3*9) - 2^5/(3*3*9*15) + + - - can be viewed as a generalized Engel-type expansion of the number 2 to the base 2. Compare with A014551. - Peter Bala, Nov 13 2013
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REFERENCES
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D. M. Burton, Elementary Number Theory, Allyn and Bacon, Inc. Boston, MA, 1976, p. 29.
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LINKS
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FORMULA
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G.f.: 3*x / ( (1+x)*(1-2*x) )
G.f.: Q(0) where Q(k)= 1 - 1/(4^k - 2*x*16^k/(2*x*4^k - 1/(1 + 1/(2*4^k - 8*x*16^k/(4*x*4^k + 1/Q(k+1) ))))); (continued fraction). - Sergei N. Gladkovskii, Apr 13 2013
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MATHEMATICA
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LinearRecurrence[{1, 2}, {0, 3}, 30] (* or *) Table[2^n - (-1)^n, {n, 0, 30}] (* G. C. Greubel, Jan 15 2018 *)
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PROG
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(PARI) for(n=0, 22, print(2^n+(-1)^(n+1)))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jul 06 2001
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STATUS
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approved
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