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%I #23 Feb 28 2018 14:07:13
%S 0,0,1,0,0,1,2,4,7,14,28,55,108,212,417,820,1612,3169,6230,12248,
%T 24079,47338,93064,182959,359688,707128,1390177,2733016,5372968,
%U 10562977
%N 5-step Fibonacci sequence starting with 0,0,1,0,0.
%H G. C. Greubel, <a href="/A251653/b251653.txt">Table of n, a(n) for n = 0..1000</a>
%H H. Prodinger, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Prodinger2/prod31.html">Counting Palindromes According to r-Runs of Ones Using Generating Functions</a>, J. Int. Seq. 17 (2014) # 14.6.2, even length, r=4.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1).
%F a(n+5) = a(n) + a(n+1) + a(n+2) + a(n+3) + a(n+4).
%F G.f.: x^2*(x^2 + x - 1)/(x^5 + x^4 + x^3 + x^2 + x - 1). - _Chai Wah Wu_, May 27 2016
%t LinearRecurrence[{1, 1, 1, 1, 1}, {0, 0, 1, 0, 0}, 100] (* _G. C. Greubel_, May 27 2016 *)
%o (J) (see www.jsoftware.com) First construct the generating matrix
%o 1 1 1 1 1
%o 1 2 2 2 2
%o 2 3 4 4 4
%o 4 6 7 8 8
%o 8 12 14 15 16
%o Given that matrix one can produce the first 5*200 numbers by
%o , M(+/ . *)^:(i.250) 0 0 1 0 0x
%Y Other 5-step sequences are A000322, A001591, A023424, A074048, A124312, A124313, A122997, A135055, A135056, A145029
%K nonn,easy
%O 0,7
%A _Arie Bos_, Dec 06 2014
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