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A017817
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a(n) = a(n-3) + a(n-4), with a(0)=1, a(1)=a(2)=0, a(3)=1.
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20
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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, 80, 92, 113, 144, 172, 205, 257, 316, 377, 462, 573, 693, 839, 1035, 1266, 1532, 1874, 2301, 2798, 3406, 4175, 5099, 6204, 7581, 9274, 11303, 13785, 16855, 20577, 25088
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OFFSET
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0,8
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COMMENTS
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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
Number of compositions (ordered partitions) of n into parts 3 and 4.
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LINKS
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FORMULA
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G.f.: 1/(1-x^3-x^4).
a(n) = Sum_{k=0..floor(n/3)} binomial(k,n-3*k). - Seiichi Manyama, Mar 06 2019
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MATHEMATICA
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LinearRecurrence[{0, 0, 1, 1}, {1, 0, 0, 1}, 60] (* G. C. Greubel, Mar 05 2019 *)
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PROG
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(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))
(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
(Sage) (1/(1-x^3-x^4)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Mar 05 2019
(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 17 1999
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STATUS
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approved
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