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%I #12 Feb 10 2021 13:53:07
%S 1,3,2,5,2,4,2,7,2,4,2,6,2,4,2,9,2,4,2,6,2,4,2,8,2,4,2,6,2,4,2,11,2,4,
%T 2,6,2,4,2,8,2,4,2,6,2,4,2,10,2,4,2,6,2,4,2,8,2,4,2,6,2,4,2,13,2,4,2,
%U 6,2,4,2,8,2,4,2,6,2,4,2,10,2,4,2,6,2,4,2,8,2,4,2,6,2,4,2,12,2,4,2,6,2,4,2,8,2,4
%N Row sums of inverse of number triangle A(n,k) = 1/(2n+1) if k <= n <= 2k, 0 otherwise.
%C Row sums of A127749.
%C Conjecture: a(n) mod 2 gives Fredholm-Rueppel sequence A036987.
%C The conjecture is true at least up to n=2048. - _Antti Karttunen_, Sep 29 2018
%H Antti Karttunen, <a href="/A127750/b127750.txt">Table of n, a(n) for n = 0..2048</a>
%t A[n_, k_] := If[k <= n <= 2k, 1/(2n+1), 0];
%t Total /@ Inverse[Array[A, {128, 128}, {0, 0}]] (* _Jean-François Alcover_, Feb 10 2021 *)
%o (PARI)
%o up_to = 128;
%o A127750aux(n,k) = if(k<=n,if(n<=(2*k),1/(n+n+1),0),0);
%o A127750list(up_to) = { my(m1=matrix(up_to,up_to,n,k,A127750aux(n-1,k-1)), m2 = matsolve(m1,matid(up_to)), v = vector(up_to)); for(n=1,up_to,v[n] = vecsum(m2[n,])); (v); };
%o v127750 = A127750list(1+up_to);
%o A127750(n) = v127750[1+n]; \\ _Antti Karttunen_, Sep 29 2018
%Y Cf. A127749, A127752.
%K nonn
%O 0,2
%A _Paul Barry_, Jan 28 2007
%E More terms from _Antti Karttunen_, Sep 29 2018
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