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A280154 a(n) = 5*Lucas(n).

%I A280154 #44 Aug 20 2022 18:48:12
%S A280154 10,5,15,20,35,55,90,145,235,380,615,995,1610,2605,4215,6820,11035,
%T A280154 17855,28890,46745,75635,122380,198015,320395,518410,838805,1357215,
%U A280154 2196020,3553235,5749255,9302490,15051745,24354235,39405980,63760215,103166195,166926410,270092605,437019015
%N A280154 a(n) = 5*Lucas(n).
%C A280154 Fibonacci sequence beginning 10, 5.
%C A280154 After 5, the sequence provides the 3rd column of the rectangular array in A213590.
%C A280154 After 5, all terms belong to A191921 because a(n) = Lucas(n+4) - 3*Lucas(n-1).
%C A280154 From _G. C. Greubel_, Dec 27 2016: (Start)
%C A280154 {a(n) mod 3} yields (1,2,0,2,2,1,0,1), repeated, and is given as A082115.
%C A280154 {a(n) mod 6} yields (4,5,3,2,5,1,0,1,1,2,3,5,2,1,3,4,1,5,0,5,5,4,3,1) and is given as A082117. (End)
%H A280154 Bruno Berselli, <a href="/A280154/b280154.txt">Table of n, a(n) for n = 0..1000</a>
%H A280154 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A280154 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A280154 G.f.: 5*(2 - x)/(1 - x - x^2).
%F A280154 a(n) = a(n-1) + a(n-2) for n>1.
%F A280154 a(n) = Fibonacci(n+5) + Fibonacci(n-5), with Fibonacci(-k) = -(-1)^k*Fibonacci(k) for the negative indices.
%p A280154 F := n -> combinat:-fibonacci(n):
%p A280154 seq(F(n+5) + F(n-5), n=0..38); # _Peter Luschny_, Dec 29 2016
%t A280154 Table[5 LucasL[n], {n, 0, 40}]
%o A280154 (PARI) vector(40, n, n--; fibonacci(n+5)+fibonacci(n-5))
%o A280154 (Magma) [5*Lucas(n): n in [0..40]];
%o A280154 (Sage)
%o A280154 def A280154():
%o A280154     x, y = 10, 5
%o A280154     while True:
%o A280154         yield x
%o A280154         x, y = y, x + y
%o A280154 a = A280154(); print([next(a) for _ in range(39)]) # _Peter Luschny_, Dec 29 2016
%Y A280154 Subsequence of A084176.
%Y A280154 Cf. A022088: 5*Fibonacci(n).
%Y A280154 Cf. A022359: Lucas(n+5) + Lucas(n-5).
%Y A280154 Cf. A000032, A000045, A191921, A213590.
%Y A280154 Cf. sequences with formula Fibonacci(n+k) + Fibonacci(n-k): A006355 (k=0, without the initial 1), A000032 (k=1), A022086 (k=2), A022112 (k=3, with an initial 4), A022090 (k=4), this sequence (k=5), A022352 (k=6).
%K A280154 nonn,easy
%O A280154 0,1
%A A280154 _Bruno Berselli_, Dec 27 2016