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A340502
Number of zeros in row n of triangle A249223.
1
0, 0, 1, 0, 1, 0, 2, 0, 1, 1, 3, 0, 3, 1, 1, 0, 4, 0, 4, 0, 2, 3, 5, 0, 3, 3, 2, 0, 6, 0, 6, 0, 3, 4, 3, 0, 7, 5, 4, 0, 7, 0, 7, 1, 1, 6, 8, 0, 5, 1, 5, 2, 8, 0, 4, 0, 6, 7, 9, 0, 9, 7, 2, 0, 4, 0, 10, 4, 7, 1, 10, 0, 10, 8, 3, 4, 5, 1, 11, 0, 4, 9, 11, 0, 6, 9, 8, 0, 11, 0, 5, 6, 9
OFFSET
1,7
COMMENTS
Equivalently, half the number of zeros in row n of A262045.
LINKS
FORMULA
a(k) = 0 iff A237271(k) = 1.
If p is an odd prime, a(p) = A003056(p) - 1 and a(p^2) = p - 2.
MAPLE
r := proc(n) floor((sqrt(1+8*n)-1)/2) ; end proc: # A003056
A237048:=proc(n, k) local i; global r;
if n<(k-1)*k/2 or k>r(n) then return(0); fi;
if (k mod 2)=1 and (n mod k)=0 then return(1); fi;
if (k mod 2)=0 and ((n-k/2) mod k) = 0 then return(1); fi;
return(0);
end;
A249223:=proc(n, k) local i; global r, A237048;
if n<(k-1)*k/2 or k>r(n) then return(0); fi;
add( (-1)^(i+1)*A237048(n, i), i=1..k);
end;
A340502 := proc(n) local ct, k; global r, A249223;
ct:=0;
for k from 1 to r(n) do if A249223(n, k)=0 then ct:=ct+1; fi; od:
ct;
end;
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 15 2021
STATUS
approved