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%I #52 Dec 19 2022 17:31:53
%S 1,0,0,1,1,0,1,2,1,1,3,3,2,4,6,5,6,10,11,11,16,21,22,27,37,43,49,64,
%T 80,92,113,144,172,205,257,316,377,462,573,693,839,1035,1266,1532,
%U 1874,2301,2798,3406,4175,5099,6204,7581,9274,11303,13785,16855,20577,25088
%N a(n) = a(n-3) + a(n-4), with a(0)=1, a(1)=a(2)=0, a(3)=1.
%C Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=3, I={0,1}. - _Vladimir Baltic_, Mar 07 2012
%C Number of compositions (ordered partitions) of n into parts 3 and 4.
%H Seiichi Manyama, <a href="/A017817/b017817.txt">Table of n, a(n) for n = 0..10000</a>
%H Vladimir Baltic, <a href="https://doi.org/10.2298/AADM1000008B">On the number of certain types of strongly restricted permutations</a>, Applicable Analysis and Discrete Mathematics 4 (2010), 119-135.
%H Johann Cigler, <a href="https://arxiv.org/abs/2212.02118">Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials</a>, arXiv:2212.02118 [math.NT], 2022.
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=484">Encyclopedia of Combinatorial Structures 484</a>
%H Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3.
%H E. Wilson, <a href="http://www.anaphoria.com/meruone.PDF">The Scales of Mt. Meru</a>
%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1).
%F G.f.: 1/(1-x^3-x^4).
%F a(n)/a(n-1) tends to A060007. - _Gary W. Adamson_, Oct 22 2006
%F a(n) = Sum_{k=0..floor(n/3)} binomial(k,n-3*k). - _Seiichi Manyama_, Mar 06 2019
%t LinearRecurrence[{0,0,1,1}, {1,0,0,1}, 60] (* _G. C. Greubel_, Mar 05 2019 *)
%o (PARI) a(n)=polcoeff(if(n<0,(1+x)/(1+x-x^4),1/(1-x^3-x^4)) +x*O(x^abs(n)), abs(n))
%o (Magma) I:=[1,0,0,1]; [n le 4 select I[n] else Self(n-3) +Self(n-4): n in [1..60]]; // _G. C. Greubel_, Mar 05 2019
%o (Sage) (1/(1-x^3-x^4)).series(x, 60).coefficients(x, sparse=False) # _G. C. Greubel_, Mar 05 2019
%o (GAP) a:=[1,0,0,1];; for n in [5..60] do a[n]:=a[n-3]+a[n-4]; od; a; # _G. C. Greubel_, Mar 05 2019
%Y A003269(n) = a(-4-n)(-1)^n.
%K nonn,easy
%O 0,8
%A _N. J. A. Sloane_
%E More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 17 1999
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