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
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
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
After 0, subsequence of A005101.
KEYWORD
nonn,easy
AUTHOR
Felix Fröhlich, Sep 07 2018
STATUS
approved