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An Euler phi transform of 1/(1 - x^2).
2

%I #14 Aug 04 2024 19:12:37

%S 0,1,1,3,3,7,5,13,9,19,13,29,17,41,23,49,31,65,37,83,45,95,55,117,63,

%T 137,75,155,87,183,95,213,111,233,127,257,139,293,157,317,173,357,185,

%U 399,205,423,227,469,243,511,263,543,287,595,305,635,329,671,357,729

%N An Euler phi transform of 1/(1 - x^2).

%F a(n) = Sum_{k=0..n} phi(n-k+1)*(k mod 2).

%F Euler transform of period 7 sequence [3,-2,-1,-1,-2,3,0,...].

%F a(2n) = A049690(n).

%F a(2n+1) = A099957(n).

%o (PARI) a(n) = sum(k=0, n, if (k%2, eulerphi(n-k+1))); \\ _Michel Marcus_, Jun 12 2024

%o (Python)

%o # uses programs from A002088 and A049690

%o def A106481(n): return A002088(n+1)-A049690(n+1>>1) if n&1 else A049690(n>>1) # _Chai Wah Wu_, Aug 04 2024

%Y Cf. A049690, A099957.

%K easy,nonn

%O 0,4

%A _Paul Barry_, May 03 2005