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%I #40 Oct 25 2017 07:36:00
%S -3,-1,4,8,15,16,23,42,66,104,162,251,397,625,980,1539,2415,3792,5956,
%T 9351,14682,23053,36196,56834,89238,140116,220003,345437,542387,
%U 851628,1337181,2099571,3296636,5176204,8127403,12761220,20036995,31461034,49398458,77562856,121785110,191220563,300244453
%N a(n) = a(n-1) + a(n-3) + a(n-5).
%C The ratio of successive terms of this sequence converges to the real root of x^5 - x^4 - x^2 - 1 which is approximately 1.5701473... (see A293506). - _Iain Fox_, Oct 12 2017
%H Robert Israel, <a href="/A122115/b122115.txt">Table of n, a(n) for n = 1..5098</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 0, 1).
%F G.f.: x*(-3 + 2*x + 5x^2 + 7*x^3 + 8*x^4)/(1 - x - x^3 - x^5). - _Philippe Deléham_, Oct 20 2006
%e -3 + 4 + 15 = 16
%e -1 + 8 + 16 = 23
%e 4 + 15 + 23 = 42
%p a[1]:=-3: a[2]:=-1: a[3]:=4: a[4]:=8: a[5]:=15: for n from 6 to 45 do a[n]:=a[n-1]+a[n-3]+a[n-5] od: seq(a[n],n=1..45); # _Emeric Deutsch_, Oct 23 2006
%t LinearRecurrence[{1,0,1,0,1},{-3,-1,4,8,15},50] (* _Harvey P. Dale_, Apr 22 2013 *)
%o (PARI) first(n) = my(res = vector(n)); res[1] = -3; res[2] = -1; res[3] = 4; res[4] = 8; res[5] = 15; for(i = 6, n, res[i] = res[i-1] + res[i-3] + res[i-5]); res \\ _Iain Fox_, Oct 23 2017
%Y This sequence includes the "Lost" numbers, 4 8 15 16 23 42, A104101. - Rick Powers (powersr(AT)westerntc.edu), Sep 18 2009
%K sign
%O 1,1
%A Jian Tang (jian.tang(AT)gmail.com), Oct 19 2006
%E More terms from _Emeric Deutsch_, Oct 23 2006
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