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 A317095 a(n) = 40*n. 0

%I

%S 0,40,80,120,160,200,240,280,320,360,400,440,480,520,560,600,640,680,

%T 720,760,800,840,880,920,960,1000,1040,1080,1120,1160,1200,1240,1280,

%U 1320,1360,1400,1440,1480,1520,1560,1600,1640,1680,1720,1760,1800,1840,1880

%N a(n) = 40*n.

%C a(n) is equal to the freshwater zone below sea level for a water table of elevation n above sea level in a simplified freshwater-saltwater interface in a coastal water-table aquifer (cf. Barlow, 2003, p. 14, eq. (2) and p. 15, Fig. B-1 and B-2).

%C From _Bruno Berselli_, Sep 10 2018: (Start)

%C After 0, subsequence of A065607: 1/a(n)^2 + 1/(30*n)^2 = 1/(24*n)^2, with n > 0 and a(n) > 30*n.

%C Also, all positive terms belong to A049094: 2^(40*n)-1 = 1024^(4*n)-1 and (25*41-1)^(4*n)-1 is divisible by 25. (End)

%H P. M. Barlow, <a href="https://doi.org/10.3133/cir1262">Ground Water in Freshwater-Saltwater Environments of the Atlantic Coast</a>, Circular 1262 (2003).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Aquifer">Aquifer</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Saltwater_intrusion">Saltwater intrusion</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F O.g.f.: 40*x/(1 - x)^2.

%F E.g.f.: 40*x*exp(x). - _Bruno Berselli_, Sep 10 2018

%F a(n) = 2*a(n - 1) - a(n - 2) for n > 1. - _Stefano Spezia_, Sep 07 2018

%F a(n) = A008586(A008592(n)) = 4*A008592(n).

%F a(n) = A010692(n)*A008586(n) = 10*A008586(n).

%F a(n) = A008602(A005843(n)) = 20*A005843(n).

%F a(n) = A007395(n)*A008602(n) = 2*A008602(n).

%t Table[40 n, {n, 0, 50}] (* or *)

%t LinearRecurrence[{2, -1}, {0, 40}, 50] (* or *)

%t CoefficientList[Series[40*x/(1 - x)^2, {x, 0, 50}], x] (* _Stefano Spezia_, Sep 07 2018 *)

%o (PARI) a(n) = 40*n

%o (PARI) a(n) = if(n==0, 0, if(n==1, 40, 2*a(n-1)-a(n-2)))

%o (PARI) concat(0, Vec(40*x/(1-x)^2 + O(x^60)))

%Y Cf. A005843, A007395, A008586, A008592, A008602, A010692, A049094, A065607.

%Y Row n = 40 of A004247. Intersection of A008587 and A008590.

%Y After 0, subsequence of A005101.

%K nonn,easy

%O 0,2

%A _Felix FrÃ¶hlich_, Sep 07 2018

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Last modified July 31 05:39 EDT 2021. Contains 346367 sequences. (Running on oeis4.)