cp's OEIS Frontend

A372847 Number of unit squares enclosed by a circle of radius n with an even number of rows and the maximum number of squares in each row.

%I A372847 #19 May 16 2024 20:34:15
%S A372847 0,6,18,36,64,92,130,172,224,284,344,410,488,570,658,750,852,956,1072,
%T A372847 1194,1312,1450,1584,1728,1882,2044,2204,2372,2548,2730,2916,3112,
%U A372847 3312,3520,3738,3950,4184,4408,4656,4900,5146,5402,5670,5942,6222,6492,6784,7080,7382,7700
%N A372847 Number of unit squares enclosed by a circle of radius n with an even number of rows and the maximum number of squares in each row.
%C A372847 Always has an even number of rows (2*n-2) and each row may have an odd or even number of squares.
%C A372847 Symmetrical about the horizontal and vertical axes.
%H A372847 David Dewan, <a href="/A372847/b372847.txt">Table of n, a(n) for n = 1..10000</a>
%H A372847 David Dewan, <a href="/A372847/a372847.pdf">Drawings for n=1..12.</a>
%F A372847 a(n) = 2*Sum_{k=1..n-1} floor(2*sqrt(n^2 - k^2)).
%e A372847 For n=4
%e A372847 row 1:   5 squares
%e A372847 row 2:   6 squares
%e A372847 row 3:   7 squares
%e A372847 row 4:   7 squares
%e A372847 row 5:   6 squares
%e A372847 row 6:   5 squares
%e A372847 Total = 36
%t A372847 a[n_]:=2 Sum[Floor[2 Sqrt[n^2 - k^2]], {k,n-1}]; Array[a,50]
%Y A372847 Cf. A136485 (by diameter), A001182 (within quadrant), A136483 (quadrant by diameter), A119677 (even number of rows with even number of squares in each), A125228 (odd number of rows with maximal squares per row), A341198 (points rather than squares).
%K A372847 nonn
%O A372847 1,2
%A A372847 _David Dewan_, May 14 2024