A295821 Number of coprime pairs (a,b) with -n <= a <= n, -2 <= b <= 2.
2, 12, 16, 24, 28, 36, 40, 48, 52, 60, 64, 72, 76, 84, 88, 96, 100, 108, 112, 120, 124, 132, 136, 144, 148, 156, 160, 168, 172, 180, 184, 192, 196, 204, 208, 216, 220, 228, 232, 240, 244, 252, 256, 264, 268, 276, 280, 288, 292, 300, 304, 312, 316, 324, 328
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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PARI
a(n) = sum(x=-n, n, sum(y=-2, 2, gcd(x,y)==1)); \\ Michel Marcus, Jan 19 2025
Formula
From Alois P. Heinz, Jan 19 2025: (Start)
G.f.: -2*(x^3-x^2-5*x-1)/((x+1)*(x-1)^2).
a(n) = 2 * A047238(n+2) for n>=1. (End)
a(n) = 6*n + 5 - (-1)^n for n>=1. - Keagan Boyce, Jan 19 2025
Sum_{n>=0} (-1)^n/a(n) = 1/4 + Pi/(24*sqrt(3)) + log(3)/8. - Amiram Eldar, Jan 23 2025