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A127752 Row sums of inverse of number triangle A(n,k) = 1/(3n+1) if k <= n <= 2k, 0 otherwise.

%I A127752 #11 Feb 11 2021 13:44:33
%S A127752 1,4,3,7,3,6,3,10,3,6,3,9,3,6,3,13,3,6,3,9,3,6,3,12,3,6,3,9,3,6,3,16,
%T A127752 3,6,3,9,3,6,3,12,3,6,3,9,3,6,3,15,3,6,3,9,3,6,3,12,3,6,3,9,3,6,3,19,
%U A127752 3,6,3,9,3,6,3,12,3,6,3,9,3,6,3,15,3,6,3,9,3,6,3,12,3,6,3,9,3,6,3,18,3,6,3,9,3,6,3,12,3,6
%N A127752 Row sums of inverse of number triangle A(n,k) = 1/(3n+1) if k <= n <= 2k, 0 otherwise.
%C A127752 Row sums of number triangle A127751.
%C A127752 a(n) mod 2 is first Feigenbaum symbolic sequence A035263 (conjecture).
%C A127752 The conjecture is true at least up to 2048 first terms. (But please note the different indexing, here 0-based.) - _Antti Karttunen_, Sep 29 2018
%H A127752 Antti Karttunen, <a href="/A127752/b127752.txt">Table of n, a(n) for n = 0..2048</a>
%t A127752 A[n_, k_] := If[k <= n <= 2k, 1/(3n+1), 0];
%t A127752 Total /@ Inverse[Array[A, {128, 128}, {0, 0}]] (* _Jean-François Alcover_, Feb 11 2021 *)
%o A127752 (PARI)
%o A127752 up_to = 128;
%o A127752 A127752aux(n,k) = if(k<=n,if(n<=(2*k),1/((3*n)+1),0),0);
%o A127752 A127752list(up_to) = { my(m1=matrix(up_to,up_to,n,k,A127752aux(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 A127752 v127752 = A127752list(1+up_to);
%o A127752 A127752(n) = v127752[1+n]; \\ _Antti Karttunen_, Sep 29 2018
%Y A127752 Cf. A127750, A127751.
%K A127752 nonn
%O A127752 0,2
%A A127752 _Paul Barry_, Jan 28 2007
%E A127752 More terms from _Antti Karttunen_, Sep 29 2018