OFFSET
1,2
COMMENTS
Analogous series using the Fibonacci numbers as a generator = A089098.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,0,-12,4,4,4,4,1).
FORMULA
(1/2) * [ (1, 4, 14, 44, 131,...) + (1, 0, 2, 0, 5,...)]; where (1, 4, 14, 44,...) = A006645, the self-convolution of the Pell series, and (1, 0, 2, 0, 5,...) = the aerated Pell series.
G.f.: -x*(2*x^3-2*x+1) / ((x^2+2*x-1)^2*(x^4+2*x^2-1)). - Colin Barker, Jul 21 2015
EXAMPLE
(1/2) * (1, 4, 14, 44, 131,...) + (1, 0, 2, 0, 5,...) = (1/2) * (2, 4, 16, 44, 136, 376,...) = (1, 2, 8, 22, 68, 188,...).
MAPLE
A178159 := proc(n)
if type (n, 'even') then
else
A006645(n+2)/2 ;
fi;
end proc: # R. J. Mathar, Jul 21 2015
PROG
(PARI) Vec(-x*(2*x^3-2*x+1)/((x^2+2*x-1)^2*(x^4+2*x^2-1)) + O(x^40)) \\ Colin Barker, Jul 21 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Dec 18 2010
EXTENSIONS
Corrected by R. J. Mathar, Jul 21 2015
STATUS
approved