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a:= proc(n) option remember; `if`(n<2, 0,

a(n-1)-2 + 4*numtheory[phi](n))

end:

seq(a(n), n=0..60); # Alois P. Heinz, May 05 2020

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a(n) = -2*(n + 1) + 4*Sum_{k=1..n} phi(k) for n > 0. (End).

a(n) = 2 * A209978(n). (End)

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Cf. A171503 (determinants of matrices that include zero), A196228A209978, A210000.

0, 0, 2, 8, 14, 28, 34, 56, 70, 92, 106, 144, 158, 204, 226, 256, 286, 348, 370, 440, 470, 516, 554, 640, 670, 748, 794, 864, 910, 1020, 1050, 1168, 1230, 1308, 1370, 1464, 1510, 1652, 1722, 1816, 1878, 2036, 2082, 2248, 2326, 2420, 2506, 2688, 2750, 2916, 2994

1,2

0,3

Andrew Howroyd, <a href="/A196227/b196227.txt">Table of n, a(n) for n = 0..1000</a>

From Andrew Howroyd, May 05 2020: (Start)

a(n) = A171503(n) - (2*n + 1) for n > 0.

a(n) = -2*(n + 1) + 4*Sum_{k=1..n} phi(k) for n > 0. (End)

(PARI) a(n) = if(n < 1, 0, 4*sum(k=1, n, eulerphi(k)) - 2*(n + 1)) \\ Andrew Howroyd, May 05 2020

Cf. A171503 (determinants of matrices that include zero).), A196228, A210000.

a(0)=0 prependend by Andrew Howroyd, May 05 2020

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Table[cnt = 0; Do[If[a*d-b*c == 1, cnt++], {a, n}, {b, n}, {c, n}, {d, n}]; cnt, {n, 50}] (* }] (* _T. D. Noe, _, Oct 11 2011 *)

OEIS Server: https://oeis.org/edit/global/2267

_Aldo González Lorenzo (gravesinha(AT)gmail.com), _, Sep 29 2011

OEIS Server: https://oeis.org/edit/global/566

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