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A051132 Number of ordered pairs of integers (x,y) with x^2+y^2 < n^2. 10

%I

%S 0,1,9,25,45,69,109,145,193,249,305,373,437,517,609,697,793,889,1005,

%T 1125,1245,1369,1513,1649,1789,1941,2109,2285,2449,2617,2809,2997,

%U 3205,3405,3613,3841,4049,4281,4509,4765,5013,5249,5521,5785,6073,6349,6621

%N Number of ordered pairs of integers (x,y) with x^2+y^2 < n^2.

%C a(n) = A000328(n) - A046109(n). [_Reinhard Zumkeller_, Jan 23 2012]

%H T. D. Noe, <a href="/A051132/b051132.txt">Table of n, a(n) for n = 0..1000</a>

%e a(3)=25 from the points of shapes 00 (1), 10 (4), 11 (4), 20 (4), 21 (8), 22 (4).

%t Table[Sum[SquaresR[2, k], {k, 0, n^2 - 1}], {n, 0, 46}]

%o (Haskell)

%o a051132 n = length [(x,y) | x <- [-n..n], y <- [-n..n], x^2 + y^2 < n^2]

%o -- _Reinhard Zumkeller_, Jan 23 2012

%Y Changing "<" to "<=" in the definition gives A000328.

%K nonn,nice,easy

%O 0,3

%A Jostein Trondal (jostein.trondal(AT)protech.no)

%E More terms from _James A. Sellers_

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Last modified February 7 07:24 EST 2023. Contains 360112 sequences. (Running on oeis4.)