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A193884
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Expansion of o.g.f. (1-x^2)/(1-x+x^4).
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2
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1, 1, 0, 0, -1, -2, -2, -2, -1, 1, 3, 5, 6, 5, 2, -3, -9, -14, -16, -13, -4, 10, 26, 39, 43, 33, 7, -32, -75, -108, -115, -83, -8, 100, 215, 298, 306, 206, -9, -307, -613, -819, -810, -503, 110, 929, 1739, 2242, 2132, 1203, -536, -2778, -4910, -6113, -5577
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OFFSET
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0,6
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COMMENTS
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The Kn11 sums, see A180662, of triangle A108299 equal the terms of this sequence.
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LINKS
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FORMULA
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G.f.: (1+x)*(1-x)/(1-x+x^4).
a(n) = a(n-1)-a(n-4), a(0) = a(1) = 1, a(2) = a(3) = 0.
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MAPLE
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A193884 := proc(n) option remember: if n=0 then 1 elif n=1 then 1 elif n=2 then 0 elif n=3 then 0 elif n>=4 then procname(n-1)-procname(n-4) fi: end: seq(A193884(n), n=0..54);
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MATHEMATICA
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CoefficientList[Series[(1-x^2)/(1-x+x^4), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, 0, 0, -1}, {1, 1, 0, 0}, 80] (* Harvey P. Dale, Jul 15 2020 *)
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CROSSREFS
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KEYWORD
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sign,easy,changed
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AUTHOR
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STATUS
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approved
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