Search: a013984 -id:a013984
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1, 0, 1, 1, 1, 2, 3, 4, 6, 10, 16, 25, 40, 63, 100, 159, 253, 402, 640, 1017, 1617, 2570, 4087, 6498, 10331, 16427, 26118, 41528, 66030, 104988, 166931, 265421, 422020, 671014, 1066916, 1696402, 2697289, 4288703, 6819061, 10842344, 17239385, 27410714, 43583183, 69297495, 110183389, 175192180, 278556508
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OFFSET
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0,6
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LINKS
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FORMULA
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MATHEMATICA
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Ceiling[CoefficientList[Series[1/(1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7), {x, 0, 50}], x]/2] (* G. C. Greubel, Nov 23 2016 *)
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CROSSREFS
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KEYWORD
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nonn,easy,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A107479
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a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7).
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+10
10
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0, 1, 1, 2, 3, 5, 8, 12, 20, 31, 50, 79, 126, 200, 318, 506, 804, 1279, 2033, 3233, 5140, 8173, 12995, 20662, 32853, 52236, 83056, 132059, 209975, 333861, 530841, 844040, 1342028, 2133832, 3392804, 5394577, 8577406, 13638122, 21684687, 34478769
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OFFSET
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0,4
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LINKS
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FORMULA
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Lim_{n->infinity} a(n)/a(n-1) = 1.5900053739...
G.f.: x*(1 + x)*(1 - x + x^2)*(1 + x + x^2)/(1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7).
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MATHEMATICA
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LinearRecurrence[{0, 1, 1, 1, 1, 1, 1}, {0, 1, 1, 2, 3, 5, 8}, 40] (* Harvey P. Dale, Sep 26 2012 *)
CoefficientList[Series[x (1 + x) (1 + x + x^2) (x^2 - x + 1)/(1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 16 2014 *)
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PROG
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(PARI) concat(0, Vec(x*(1+x)*(1+x+x^2)*(x^2-x+1)/(1-x^2-x^3-x^4-x^5-x^6-x^7) + O(x^60))) \\ Michel Marcus, Oct 16 2014
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1+x)*(1+x+x^2)*(x^2-x+1)/(1-x^2-x^3-x^4-x^5-x^6-x^7) )); // G. C. Greubel, Nov 03 2018
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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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Definition replaced by recurrence - The Associate Editors of the OEIS, Oct 02 2009
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STATUS
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approved
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A107480
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a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-7).
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+10
10
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0, 1, 1, 2, 3, 5, 8, 14, 25, 42, 71, 121, 207, 353, 601, 1025, 1748, 2980, 5080, 8661, 14767, 25176, 42922, 73178, 124762, 212707, 362644, 618273, 1054096, 1797131, 3063933, 5223708, 8905915, 15183719, 25886764, 44134416, 75244889, 128285220, 218713827
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OFFSET
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0,4
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COMMENTS
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Lim_{n->infinity} a(n)/a(n-1) = 1.70490277..., the real root of x^5 = x^4 + x^3 + 1.
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LINKS
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FORMULA
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G.f.: x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)). - Colin Barker, Dec 17 2017
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MATHEMATICA
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LinearRecurrence[{1, 0, 1, 1, 1, 0, 1}, {0, 1, 1, 2, 3, 5, 8}, 50] (* Harvey P. Dale, May 21 2012 *)
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PROG
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(PARI) concat([0], Vec(x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)) + O(x^40))) \\ Colin Barker, Dec 17 2017
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1 +x^2-x^5)/((1+x^2)*(1-x-x^2-x^5)))); // G. C. Greubel, Nov 03 2018
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CROSSREFS
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KEYWORD
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nonn,easy,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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