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A113435
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a(n) = a(n-1) + Sum_{k=0..n/3} a(n-3k) with a(0)=1.
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7
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1, 1, 1, 2, 3, 4, 7, 11, 16, 26, 41, 62, 98, 154, 237, 371, 581, 901, 1406, 2197, 3418, 5329, 8317, 12956, 20196, 31501, 49096, 76532, 119338, 186029, 289997, 452141, 704861, 1098826, 1713111, 2670692, 4163483, 6490879, 10119152, 15775426
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OFFSET
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0,4
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COMMENTS
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If presented in three rows a(3n), a(3n+1) and a(3n+2) each term is the sum of the previous term in the sequence and the partial sum of its row.
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LINKS
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FORMULA
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a(n) = a(n-1) + 2*a(n-3) - a(n-4) = 7*a(n-3) - 5*a(n-6) + 11*a(n-9) - a(n-12).
G.f.: (1-x^3)/(1-x-2*x^3+x^4).
G.f.: 1/(1-x) + x^3*Q(0)/(2-2*x) , where Q(k) = 1 + 1/(1 - x*(4*k+1 + 2*x^2 - x^3)/( x*(4*k+3 + 2*x^2 - x^3 ) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 11 2013
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MATHEMATICA
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CoefficientList[Series[(1 - x^3)/(1 - x - 2*x^3 + x^4), {x, 0, 50}], x] (* G. C. Greubel, Mar 10 2017 *)
LinearRecurrence[{1, 0, 2, -1}, {1, 1, 1, 2}, 40] (* Harvey P. Dale, Dec 17 2023 *)
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PROG
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(PARI) x='x+O(x^50); Vec((1 - x^3)/(1 - x - 2*x^3 + x^4)) \\ G. C. Greubel, Mar 10 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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STATUS
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approved
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