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A036702 a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n, a>=0, 0<=b<=a. 5
1, 2, 4, 7, 10, 15, 20, 25, 32, 40, 49, 57, 66, 78, 89, 102, 114, 128, 142, 158, 175, 190, 209, 227, 245, 267, 288, 310, 331, 354, 379, 402, 429, 455, 483, 512, 538, 569, 597, 631, 663, 693, 727, 761, 798, 834, 868, 906, 943, 983 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Row sums of the irregular triangle A255250. - Wolfdieter Lang, Mar 15 2015
LINKS
FORMULA
a(n) - A036700(n) = 1+A049472(n). - R. J. Mathar, Oct 29 2011
a(n) = sum(floor(sqrt(n^2 - m^2)) - (m-1), m = 0.. floor(n/sqrt(2))), n >= 0. See A255250. - Wolfdieter Lang, Mar 15 2015
MAPLE
A036702 := proc(n)
local a, x, y ;
a := 0 ;
for x from 0 do
if x^2 > n^2 then
return a;
fi ;
for y from 0 to x do
if y^2+x^2 <= n^2 then
a := a+1 ;
end if;
end do;
end do:
end proc: # R. J. Mathar, Oct 29 2011
MATHEMATICA
a[n_] := Module[{a, b}, If[n == 0, 1, Reduce[a^2 + b^2 <= n^2 && a >= 0 && 0 <= b <= a, {a, b}, Integers] // Length]];
a /@ Range[0, 49] (* Jean-François Alcover, Oct 17 2019 *)
CROSSREFS
Sequence in context: A095116 A027384 A022939 * A007983 A049640 A179385
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 23 18:16 EDT 2024. Contains 371916 sequences. (Running on oeis4.)