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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

G. C. Greubel, Table of n, a(n) for n = 1..1000

W. Bosma, Signed bits and fast exponentiation, Journal de Théorie des Nombres de Bordeaux, Vol. 13, Fasc. 1 (2001), p. 38 (Proposition 7).

Index entries for linear recurrences with constant coefficients, signature (4,-3,-4,4).

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

Cf. A073371, A127976, A127978, A127979, A127980, A073371.

Sequence in context: A213578 A212149 A208740 * A296303 A089453 A057159

Adjacent sequences:  A127978 A127979 A127980 * A127982 A127983 A127984

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Feb 09 2007

STATUS

approved

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)