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a(n) is the number of points with integer coordinates located strictly between the parabolas y = n - x^2 and y = x^2 - n.
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%I #21 Jan 19 2024 14:54:20

%S 1,5,11,17,25,35,45,55,65,77,91,105,119,133,147,161,177,195,213,231,

%T 249,267,285,303,321,341,363,385,407,429,451,473,495,517,539,561,585,

%U 611,637,663,689,715,741,767,793,819,845,871,897,925,955,985,1015,1045,1075,1105,1135,1165,1195

%N a(n) is the number of points with integer coordinates located strictly between the parabolas y = n - x^2 and y = x^2 - n.

%H Nicolay Avilov, <a href="/A368874/a368874.jpg">Illustration for terms a(1)-a(6)</a>

%F a(n) = 2*A095875(n-2) + A001650(n).

%e For n=1, one point (0,0) lies between the parabolas y = 1 - x^2 and y = x^2 - 1, so that a(1) = 1.

%Y Cf. A001650, A095875.

%K nonn

%O 1,2

%A _Nicolay Avilov_, Jan 08 2024