OFFSET
1,1
COMMENTS
Convergent a(n+1)/a(n) = ((1+sqrt(5))/2)*(1+sqrt(2)) = (1.618...)*(2.414213...) = 3.9062796... = (1 + sqrt(2) + sqrt(5) + sqrt(10))/2.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,7,2,-1).
FORMULA
a(n) = 2*A085292(n).
a(n) = (((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n) * ((1+sqrt(2))^n + (1-sqrt(2))^n).
From Colin Barker, Oct 15 2013: (Start)
a(n) = 2*a(n-1) + 7*a(n-2) + 2*a(n-3) - a(n-4).
G.f.: -2*x*(2*x^3 - 3*x^2 - 7*x - 1) / (x^4 - 2*x^3 - 7*x^2 - 2*x + 1). (End)
E.g.f.: 4*(exp(x/2)*(cosh(x/sqrt(2))*cosh(sqrt(5/2)*x)*cosh(sqrt(5)*x/2)+sinh(x/sqrt(2))*sinh(sqrt(5/2)*x)*sinh(sqrt(5)*x/2))-1). - Stefano Spezia, Aug 25 2019
PROG
(Magma) I:=[2, 18, 56, 238]; [n le 4 select I[n] else 2*Self(n-1) + 7*Self(n-2) + 2*Self(n-3) - Self(n-4):n in [1..30]]; // Marius A. Burtea, Aug 25 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 24 2003
EXTENSIONS
More terms from David Wasserman, Jan 31 2005
More terms from Colin Barker, Oct 16 2013
STATUS
approved