OFFSET
1,3
COMMENTS
Equals A001045, [1, 1, 3, 5, 11, 21, 43, 85, ...] convolved with A078008, [1, 0, 2, 2, 6, 10, 22, ...]. - Gary W. Adamson, May 25 2009
LINKS
Vincenzo Librandi, 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 (2,3,-4,-4).
FORMULA
From Joerg Arndt, May 27 2011: (Start)
a(n) = +2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4).
G.f.: x*(1-x)/((1+x)^2*(1-2*x)^2). (End)
E.g.f.: 2*exp(x/2)*(6*x*cosh(3*x/2) + 5*sinh(3*x/2))/27. - Stefano Spezia, May 25 2023
MATHEMATICA
Table[((6n + 10)/27)2^(n - 1) + ((-1)^(n - 1) )(6n + 5)/27, {n, 1, 100}]
PROG
(Magma) [((6*n + 10)/27)*2^(n - 1) + ((-1)^(n - 1))*(6*n + 5)/27: n in [1..40]]; // Vincenzo Librandi, May 26 2011
(PARI) x='x+O('x^30); Vec(x*(1-x)/((1+x)^2*(1-2*x)^2)) \\ G. C. Greubel, May 07 2018
(PARI) a(n) = ((6*n + 10)/27)*2^(n - 1) + (-1)^(n - 1)*(6*n + 5)/27; \\ Michel Marcus, May 09 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Feb 09 2007
EXTENSIONS
Name edited by Altug Alkan, May 09 2018
STATUS
approved