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A127981 a(n) = (n + 1/3)*2^(n-1) - 1/2 + (-1)^(n-1)*(1/6). 5
1, 4, 13, 34, 85, 202, 469, 1066, 2389, 5290, 11605, 25258, 54613, 117418, 251221, 535210, 1135957, 2402986, 5068117, 10660522, 22369621, 46836394, 97867093, 204122794, 425022805, 883600042, 1834308949, 3802835626, 7874106709 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
W. Bosma, Signed bits and fast exponentiation, Journal de Théorie des Nombres de Bordeaux, Vol. 13, Fasc. 1 (2001), p. 38 (Proposition 7).
FORMULA
G.f.: x*(1-2*x^3)/((1-x)*(1+x)*(1-2*x)^2). - Colin Barker, Apr 02 2012
MATHEMATICA
Table[(n+1/3)*2^(n-1) -1/2 +(-1)^(n-1)*(1/6), {n, 1, 50}]
LinearRecurrence[{4, -3, -4, 4}, {1, 4, 13, 34}, 50] (* G. C. Greubel, May 08 2018 *)
PROG
(PARI) for(n=1, 50, print1((n+1/3)*2^(n-1) -1/2 +(-1)^(n-1)*(1/6), ", ")) \\ G. C. Greubel, May 08 2018
(Magma) [(n+1/3)*2^(n-1) -1/2 +(-1)^(n-1)*(1/6): n in [1..50]]; // G. C. Greubel, May 08 2018
CROSSREFS
Sequence in context: A212149 A357284 A208740 * A296303 A089453 A057159
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Feb 09 2007
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)