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 A286350 a(n) = 2*a(n-1) - a(n-2) + a(n-4) for n>3, a(0)=0, a(1)=a(2)=2, a(3)=3. 2
 0, 2, 2, 3, 4, 7, 12, 20, 32, 51, 82, 133, 216, 350, 566, 915, 1480, 2395, 3876, 6272, 10148, 16419, 26566, 42985, 69552, 112538, 182090, 294627, 476716, 771343, 1248060, 2019404, 3267464, 5286867, 8554330, 13841197, 22395528, 36236726, 58632254, 94868979 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is b(n) in A286311(n). As mentioned in A286311, the pair A286311(n) and, here a(n), are autosequences of the first kind. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1). FORMULA a(n) = A286311(n) + A128834(n). a(n) = A022086(n) - A286311(n). a(n) = (A022086(n) + A128834(n))/2. G.f.: x*(2 - 2*x + x^2) / ((1 - x + x^2)*(1 - x - x^2)). - Colin Barker, May 09 2017 MATHEMATICA LinearRecurrence[{2, -1, 0, 1}, {0, 2, 2, 3}, 40] (* or *) CoefficientList[Series[x (2 - 2 x + x^2)/((1 - x + x^2) (1 - x - x^2)), {x, 0, 39}], x] (* Michael De Vlieger, May 09 2017 *) PROG (PARI) concat(0, Vec(x*(2 - 2*x + x^2) / ((1 - x + x^2)*(1 - x - x^2)) + O(x^60))) \\ Colin Barker, May 09 2017 (Magma) I:=[0, 2, 2, 3]; [n le 4 select I[n] else 2*Self(n-1) - Self(n-2) + Self(n-4): n in [1..30]]; // G. C. Greubel, Jan 15 2018 CROSSREFS Cf. A022086, A128834, A226956 (same recurrence), A286311. Sequence in context: A173433 A053638 A051920 * A023105 A281723 A011784 Adjacent sequences: A286347 A286348 A286349 * A286351 A286352 A286353 KEYWORD nonn,easy AUTHOR Paul Curtz, May 08 2017 EXTENSIONS More terms from Colin Barker, May 09 2017 STATUS approved

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Last modified June 2 17:31 EDT 2023. Contains 363100 sequences. (Running on oeis4.)