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A274759
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Modified quadranacci series.
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1
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0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 6, 7, 8, 12, 14, 15, 23, 27, 29, 44, 52, 56, 85, 100, 108, 164, 193, 208, 316, 372, 401, 609, 717, 773, 1174, 1382, 1490, 2263, 2664, 2872, 4362, 5135, 5536, 8408, 9898, 10671, 16207, 19079, 20569, 31240, 36776, 39648, 60217, 70888, 76424, 116072, 136641
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OFFSET
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0,6
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,0,1,0,0,1,0,0,1).
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FORMULA
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a(3n) = a(3n-3) + a(3n-6) + a(3n-9) + a(3n-12).
a(3n + 2) = a(3n + 1) + a(3n - 2).
a(3n + 3) = a(3n + 1) + a(3n - 1).
a(3n + 4) = a(3n + 1) + a(3n).
G.f.: x*(1 + x + x^2 + x^4 + x^5 + x^8)/(1 - x^3 - x^6 - x^9 - x^12).
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MATHEMATICA
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CoefficientList[Series[x*(1 + x + x^2 + x^4 + x^5 + x^8)/(1 - x^3 - x^6 - x^9 - x^12), {x, 0, 25}], x] (* or *) LinearRecurrence[{0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1}, {0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 6}, 50]
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PROG
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(PARI) concat(0, Vec(x*(1+x+x^2+x^4+x^5+x^8)/(1-x^3-x^6-x^9-x^12) + O(x^99))) \\ Altug Alkan, Jul 04 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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