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A193885
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) - a(n-4), n>=4; a(0) = 1, a(1) = 1, a(2) = 2, a(3) = 3.
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2
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1, 1, 2, 3, 3, 1, -5, -18, -41, -75, -115, -143, -118, 35, 431, 1213, 2499, 4254, 6047, 6665, 3609, -7375, -32334, -77933, -147781, -234503, -305765, -283634, -20329, 718653, 2239077, 4824577, 8495482, 12533139, 14698471, 10166901, -9557053, -57006530
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OFFSET
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0,3
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COMMENTS
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The Ze1 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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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) - a(n-4), n>=4; a(0) = 1, a(1) = 1, a(2) = 2, a(3) = 3.
G.f.: (1-x)*(1-x+x^2)/(1-3*x+3*x^2-x^3+x^4).
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MAPLE
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A193885 := proc(n) option remember: if n=0 then 1 elif n=1 then 1 elif n=2 then 2 elif n=3 then 3 elif n>=4 then 3*procname(n-1)-3*procname(n-2)+procname(n-3)-procname(n-4) fi: end: seq(A193885(n), n=0..37);
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MATHEMATICA
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CoefficientList[Series[(1-x)*(1-x+x^2)/(1-3*x+3*x^2-x^3+x^4), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 10 2012 *)
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PROG
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(Magma)I:=[1, 1, 2, 3 ]; [n le 4 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jul 10 2012
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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