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A290739 a(n) = 0 unless n = 3j^2+2j or 3j^2+4j+1 for some j>=0, in which case a(n) = (-1)^(j+1). 6

%I

%S -1,-1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,

%T 0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,

%U -1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0

%N a(n) = 0 unless n = 3j^2+2j or 3j^2+4j+1 for some j>=0, in which case a(n) = (-1)^(j+1).

%C Andrews (2016), Theorem 2, shows that A008443(n) = A290735(n) + A290737(n) + A290739(n).

%H Antti Karttunen, <a href="/A290739/b290739.txt">Table of n, a(n) for n = 0..65537</a>

%H George E. Andrews, <a href="http://www.personal.psu.edu/gea1/pdf/320.pdf">The Bhargava-Adiga Summation and Partitions</a>, preprint 2016. See Th. 2.

%H George E. Andrews, <a href="https://doi.org/10.18311/jims/2017/15836">The Bhargava-Adiga Summation and Partitions</a>, The Journal of the Indian Mathematical Society, Volume 84, Issue 3-4, 2017.

%p eps:=Array(0..120,0);

%p for j from 0 to 120 do

%p if 3*j^2+2*j <= 120 then eps[3*j^2+2*j] := (-1)^(j+1); fi;

%p if 3*j^2+4*j+1 <= 120 then eps[3*j^2+4*j+1] := (-1)^(j+1); fi;

%p od;

%o (PARI)

%o up_to = 65537;

%o A290739list(up_to) = { my(v=vector(1+up_to), c1, c2); for(j=0,oo, c1 = ((3*j*j)+j+j); if(c1>up_to, return(v), v[1+c1] = (-1)^(1+j)); c2 = ((3*j*j) + (4*j) + 1); if(c2<=up_to, v[1+c2] = (-1)^(1+j))); };

%o v290739 = A290739list(up_to);

%o A290739(n) = v290739[1+n]; \\ _Antti Karttunen_, Jan 03 2019

%Y Cf. A008443, A290733, A290734, A290735, A290736, A290737, A290738, A290739.

%Y Cf. A000567, A045944.

%K sign

%O 0

%A _N. J. A. Sloane_, Aug 10 2017

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Last modified February 23 15:45 EST 2020. Contains 332167 sequences. (Running on oeis4.)