A317095 a(n) = 40*n.

0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880

Offset

0,2

Comments

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).

From Bruno Berselli, Sep 10 2018: (Start)

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.

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)

Links

Table of n, a(n) for n=0..47.

P. M. Barlow, Ground Water in Freshwater-Saltwater Environments of the Atlantic Coast, Circular 1262 (2003).

Wikipedia, Aquifer

Wikipedia, Saltwater intrusion

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

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

E.g.f.: 40*x*exp(x). - Bruno Berselli, Sep 10 2018

a(n) = 2*a(n - 1) - a(n - 2) for n > 1. - Stefano Spezia, Sep 07 2018

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

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

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

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

Mathematica

Table[40 n, {n, 0, 50}] (* or *)
LinearRecurrence[{2, -1}, {0, 40}, 50] (* or *)
CoefficientList[Series[40*x/(1 - x)^2, {x, 0, 50}], x] (* Stefano Spezia, Sep 07 2018 *)

Prog

(PARI) a(n) = 40*n
(PARI) a(n) = if(n==0, 0, if(n==1, 40, 2*a(n-1)-a(n-2)))
(PARI) concat(0, Vec(40*x/(1-x)^2 + O(x^60)))

Crossrefs

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

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

After 0, subsequence of A005101.

Sequence in context: A253692 A253699 A037975 * A039468 A181458 A069070

Adjacent sequences: A317092 A317093 A317094 * A317096 A317097 A317098

Keyword

nonn,easy

Author

Felix Fröhlich, Sep 07 2018

Status

approved