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A277252
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a(n) = a(n-2) + a(n-3) + a(n-4) with a(0) = 0, a(1) = a(2) = 1, a(3) = 0.
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1
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0, 1, 1, 0, 2, 2, 3, 4, 7, 9, 14, 20, 30, 43, 64, 93, 137, 200, 294, 430, 631, 924, 1355, 1985, 2910, 4264, 6250, 9159, 13424, 19673, 28833, 42256, 61930, 90762, 133019, 194948, 285711, 418729, 613678, 899388, 1318118, 1931795, 2831184, 4149301, 6081097, 8912280, 13061582, 19142678, 28054959
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OFFSET
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0,5
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COMMENTS
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Limit a(n+1)/a(n) = 1.465571... (as in Narayana's cows sequence A000930).
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LINKS
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FORMULA
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a(n) = a(n - 2) + a(n - 3) + a(n - 4).
G.f.: x*(1 + x - x^2)/(1 - x^2 - x^3 - x^4).
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MAPLE
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a:= n-> (<<0|1|0|0>, <0|0|1|0>,
<0|0|0|1>, <1|1|1|0>>^n. <<0, 1, 1, 0>>)[1, 1]:
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MATHEMATICA
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CoefficientList[Series[x*(1 + x - x^2)/(1 - x^2 - x^3 - x^4), {x, 0, 50}], x]
RecurrenceTable[{a[n] == a[n - 2] + a[n - 3] + a[n - 4], a[1] == 0, a[2] == a[3] == 1, a[4] == 0}, a, {n, 52}]
LinearRecurrence[{0, 1, 1, 1}, {0, 1, 1, 0}, 52]
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PROG
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(PARI) x='x+O('x^50); concat([0], Vec(x*(1+x-x^2)/(1-x^2-x^3-x^4))) \\ G. C. Greubel, May 02 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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