A127982 Numbers of the form (n - 1/3)2^(n) - n/2 + 1/4 + (-1)^n/12.

1, 6, 20, 57, 147, 360, 850, 1959, 4433, 9894, 21840, 47781, 103759, 223908, 480590, 1026723, 2184525, 4631202, 9786700, 20621985, 43341131, 90876576, 190141770, 397060767, 827675977, 1722460830, 3579139400, 7426714269, 15390299463

Offset

1,2

Links

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

W. Bosma, Signed bits and fast exponentiation, J. Th. des Nombres de Bordeaux Vol.13, Fasc. 1, 2001.

Index entries for linear recurrences with constant coefficients, signature (5,-7,-1,8,-4).

Formula

a(n) = (n - 1/3)2^(n) - n/2 + 1/4 + (-1)^n/12.

G.f.: -x*(3*x^2-x-1)/((1+x)*(2*x-1)^2*(x-1)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009 [checked and corrected by R. J. Mathar, Sep 16 2009]

Mathematica

Table[(n-1/3)*2^n -n/2 +1/4 +(-1)^n/12, {n, 1, 50}]
LinearRecurrence[{5, -7, -1, 8, -4}, {1, 6, 20, 57, 147}, 50] (* G. C. Greubel, May 08 2018 *)

Prog

(PARI) for(n=1, 50, print1((n-1/3)*2^n -n/2 +1/4 +(-1)^n/12, ", ")) \\ G. C. Greubel, May 08 2018
(Magma) [(n-1/3)*2^n -n/2 +1/4 +(-1)^n/12: n in [1..50]]; // G. C. Greubel, May 08 2018

Crossrefs

Cf. A073371, A127976, A127978, A127979, A127980, A073371, A000337.

Sequence in context: A048611 A292480 A200528 * A109164 A212689 A027984

Adjacent sequences: A127979 A127980 A127981 * A127983 A127984 A127985

Keyword

nonn

Author

Artur Jasinski, Feb 09 2007

Status

approved