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%I #16 Feb 23 2014 14:23:14
%S 1,7,44,268,1609,9583,56792,335448,1976689,11627735,68308580,
%T 400870468,2350563097,13773547487,80663415344,472175746096,
%U 2762854639585,16160861104423,94502471413916,552472329537660
%N Total area of all 1-histograms of length n.
%C Arises in analysis of first-come-first-served (FCFS) printer policy.
%H Fung Lam, <a href="/A094113/b094113.txt">Table of n, a(n) for n = 1..1300</a>
%H D. Merlini, R. Sprugnoli and M. C. Verri, <a href="http://local.disia.unifi.it/merlini/papers/Specialfun01.ps">Waiting patterns for a printer</a>, FUN with algorithm'01, Isola d'Elba, 2001.
%H D. Merlini, R. Sprugnoli and M.C. Verri, <a href="http://dx.doi.org/10.1016/j.dam.2003.11.012">Waiting patterns for a printer</a>, Discrete Applied Mathematics, Volume 144, 359-373, 2004
%F G.f.: (1+x-sqrt(1-6*x+x^2))/(4*(1-6*x+x^2)).
%F 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
%F 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
%F a(n) ~ (sqrt(2)-1)/8 * (3+2*sqrt(2))^(n+1). - _Vaclav Kotesovec_, Feb 23 2014
%t 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 *)
%Y Cf. A001003, A035026.
%K nonn
%O 1,2
%A _Ralf Stephan_, May 03 2004
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