OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (8,-12,-4,1).
FORMULA
a(n) = sqrt(((17 + 12*sqrt(2))^n + (17 - 12*sqrt(2))^n - 2)/32) + ((1 + sqrt(2))^n - (1 - sqrt(2))^n)/(2*sqrt(2)). - Stefan Steinerberger, Jun 17 2007
From G. C. Greubel, Mar 11 2017: (Start)
a(n) = sqrt((Q_{4*n} - 2)/32) + P_{n}, where P_{n} and the Pell numbers and Q_{n} are the Pell-Lucas numbers.
a(n) = 8*a(n-1) - 12*a(n-2) - 4*a(n-3) + a(n-4).
G.f.: (2*x)*(1-4*x) / ((1-2*x-x^2)*(1-6*x+x^2)). (End)
MATHEMATICA
Simplify[Table[Sqrt[((17 + 12*Sqrt[2])^n + (17 - 12*Sqrt[2])^n - 2)/32] + ((1 + Sqrt[2])^n - (1 - Sqrt[2])^n)/(2*Sqrt[2]), {n, 1, 25}]] (* Stefan Steinerberger, Jun 17 2007 *)
Table[Sqrt[(LucasL[4*n, 2] - 2)/32] + Fibonacci[n, 2], {n, 1, 50}] (* G. C. Greubel, Mar 11 2017 *)
PROG
(PARI) x='x+O('x^50); Vec((2*x)*(1-4*x) / ((1-2*x-x^2)*(1-6*x+x^2))) \\ G. C. Greubel, Mar 11 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
K. B. Subramaniam (subramaniam_kb05(AT)yahoo.co.in), Nov 02 2005
EXTENSIONS
More terms from Stefan Steinerberger, Jun 17 2007
STATUS
approved