cp's OEIS Frontend

A285766 Maximum spillway height for a zero or one bend minimal area lake in a number square.

%I A285766 #34 May 14 2017 00:20:43
%S A285766 0,0,6,10,15,22,31,42,55,70,87,106,127,150,175,202,231,262,295,330,
%T A285766 367,406,447,490,535,582,631,682,735,790,847,906,967,1030,1095,1162,
%U A285766 1231,1302,1375,1450,1527,1606,1687,1770,1855,1942,2031,2122,2215,2310,2407
%N A285766 Maximum spillway height for a zero or one bend minimal area lake in a number square.
%C A285766 The water retention model for mathematical surfaces led to definitions for a lake and a pond.  These lakes and ponds divide the square up in interesting ways. This sequence looks at the spillway heights in zero or one bend minimal area lakes.
%C A285766 A lake has dimensions of (n-2) X (n-2) when the square is n X n.  All other water retaining areas are ponds.
%C A285766 A number square contains the numbers 1 to n^2 without repeats.
%C A285766 The larger terms are a(n)= n^2+6 or A114949.
%H A285766 Craig Knecht, <a href="/A285766/a285766_1.png">Minimal lake types in a 7x7 square.</a>
%H A285766 Craig Knecht, <a href="/A285766/a285766.png">Minimal lake area in a square</a>
%H A285766 Wikipedia, <a href="http://en.wikipedia.org/wiki/Water_retention_on_mathematical_surfaces">Water retention on mathematical surfaces</a>
%F A285766 Conjectures from _Colin Barker_, May 07 2017: (Start)
%F A285766 G.f.: x^2*(6 - 8*x + 3*x^2 + x^3) / (1 - x)^3.
%F A285766 a(n) = 7 - 2*n + n^2 for n>2.
%F A285766 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
%F A285766 (End)
%e A285766 For the 4 X 4 square a example of a smallest lake is shown. The values 1,2,3 form the lake. The pathway of least resistance off the square is the spillway value 10.
%e A285766    ( 4  16  15   5)
%e A285766    (10   1   2  14)
%e A285766    ( 6  11   3  13)
%e A285766    ( 7   8  12   9)
%Y A285766 Cf. A054247, A201126, A268311.
%K A285766 nonn
%O A285766 0,3
%A A285766 _Craig Knecht_, May 04 2017