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A094113
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Total area of all 1-histograms of length n.
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1
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1, 7, 44, 268, 1609, 9583, 56792, 335448, 1976689, 11627735, 68308580, 400870468, 2350563097, 13773547487, 80663415344, 472175746096, 2762854639585, 16160861104423, 94502471413916, 552472329537660
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OFFSET
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1,2
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COMMENTS
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Arises in analysis of first-come-first-served (FCFS) printer policy.
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LINKS
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FORMULA
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G.f.: (1+x-sqrt(1-6*x+x^2))/(4*(1-6*x+x^2)).
Recurrence: (n+1)*a(n) = (8-n)*a(n-10) + 3*(10*n-71)*a(n-9) + (2263-365*n)*a(n-8) + 4*(570*n-3021)*a(n-7) + 2*(16654-3785*n)*a(n-6) + 6138*(2*n-7)*a(n-5) + 2*(9841-3785*n)*a(n-4) + 4*(570*n-969)*a(n-3) + (292-365*n)*a(n-2) + 3*(10*n+1)*a(n-1), n>=10. - Fung Lam, Feb 07 2014
Recurrence (of order 4): n*a(n) = 3*(4*n-3)*a(n-1) - 19*(2*n-3)*a(n-2) + 3*(4*n-9)*a(n-3) - (n-3)*a(n-4). - Vaclav Kotesovec, Feb 23 2014
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MATHEMATICA
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Rest[CoefficientList[Series[(1+x-Sqrt[1-6*x+x^2])/(4*(1-6*x+x^2)), {x, 0, 20}], x]] (* Vaclav Kotesovec, Feb 23 2014 *)
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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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