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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
-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, 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, -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
OFFSET
0
COMMENTS
Andrews (2016), Theorem 2, shows that A008443(n) = A290735(n) + A290737(n) + a(n).
LINKS
George E. Andrews, The Bhargava-Adiga Summation and Partitions, preprint 2016. See Th. 2.
George E. Andrews, The Bhargava-Adiga Summation and Partitions, The Journal of the Indian Mathematical Society, Volume 84, Issue 3-4, 2017.
MAPLE
eps:=Array(0..120, 0);
for j from 0 to 120 do
if 3*j^2+2*j <= 120 then eps[3*j^2+2*j] := (-1)^(j+1); fi;
if 3*j^2+4*j+1 <= 120 then eps[3*j^2+4*j+1] := (-1)^(j+1); fi;
od;
PROG
(PARI)
up_to = 65537;
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))); };
v290739 = A290739list(up_to);
A290739(n) = v290739[1+n]; \\ Antti Karttunen, Jan 03 2019
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Aug 10 2017
STATUS
approved