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A052938
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Expansion of (1 + 2*x - 2*x^2)/( (1+x)*(1-x)^2 ).
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12
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1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 20, 19, 21, 20, 22, 21, 23, 22, 24, 23, 25, 24, 26, 25, 27, 26, 28, 27, 29, 28, 30, 29, 31, 30, 32, 31, 33, 32, 34, 33, 35, 34, 36, 35, 37, 36, 38, 37, 39
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1+2*x-2*x^2)/((1+x)*(1-x)^2).
a(n) = -a(n-1) + n + 3, with a(0)=1.
a(n) = (3*(-1)^(n+1) + 2*n + 7)/4.
E.g.f.: ((5+x)*sinh(x) + (2+x)*cosh(x))/2. - G. C. Greubel, Oct 18 2019
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MAPLE
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spec := [S, {S=Prod(Union(Sequence(Z), Z, Z), Sequence(Prod(Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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MATHEMATICA
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LinearRecurrence[{1, 1, -1}, {1, 3, 2}, 80] (* Harvey P. Dale, Apr 10 2019 *)
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PROG
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(Haskell)
a052938 n = a052938_list !! n
a052938_list = 1 : 3 : 2 : zipWith (-) [5..] a052938_list
(Magma) [(2*n+7-3*(-1)^n)/4: n in [0..30]]; // G. C. Greubel, Oct 18 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 75); Coefficients(R!( (1 + 2*x - 2*x^2)/( (1+x)*(1-x)^2 ))); // Marius A. Burtea, Oct 18 2019
(Sage) [(2*n+7-3*(-1)^n)/4 for n in (0..30)] # G. C. Greubel, Oct 18 2019
(GAP) List([0..30], n-> (2*n+7-3*(-1)^n)/4); # G. C. Greubel, Oct 18 2019
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CROSSREFS
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Cf. A028242 (same sequence with 1,0,2 prefix).
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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