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A133641
a(n) = 2*L(n) + L(n-1) - n, L(n) = n-th Lucas number A000204(n).
0
1, 5, 8, 14, 24, 41, 69, 115, 190, 312, 510, 831, 1351, 2193, 3556, 5762, 9332, 15109, 24457, 39583, 64058, 103660, 167738, 271419, 439179, 710621, 1149824, 1860470, 3010320, 4870817, 7881165, 12752011, 20633206, 33385248, 54018486, 87403767, 141422287, 228826089, 370248412
OFFSET
1,2
COMMENTS
Limit_{n->infinity} a(n)/a(n-1) = phi.
FORMULA
Given n-th Lucas number A000204(n), a(n) = 2*L(n) + L(n-1) - n.
G.f.: -x*(1-5*x^2+x^3+2*x+2*x^4)/(-1+x+x^2)/(-1+x)^2. - R. J. Mathar, Nov 14 2007
a(n) = A000032(n+2) - n = Fibonacci(n+3) + Fibonacci(n+1) - n, n > 1. - R. J. Mathar, Jul 20 2009, extended by David A. Corneth, Aug 08 2018
EXAMPLE
a(5) = 24 = 2*L(5) + L(4) - n = 2*11 + 7 - 5.
MATHEMATICA
a[1] = 1; a[n_] := LucasL[n+2] - n;
Array[a, 14] (* Jean-François Alcover, Aug 08 2018, after R. J. Mathar *)
PROG
(PARI) a(n) = {if(n==1, 1, fibonacci(n+3)+fibonacci(n+1)-n)} \\ David A. Corneth, Aug 08 2018
CROSSREFS
Sequence in context: A124011 A101835 A192522 * A164094 A246319 A302649
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Sep 19 2007
STATUS
approved