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A127773 Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.

%I A127773 #33 Jun 11 2025 03:20:44
%S A127773 1,0,3,0,0,6,0,0,0,10,0,0,0,0,15,0,0,0,0,0,21,0,0,0,0,0,0,28,0,0,0,0,
%T A127773 0,0,0,36,0,0,0,0,0,0,0,0,45,0,0,0,0,0,0,0,0,0,55,0,0,0,0,0,0,0,0,0,0,
%U A127773 66,0,0,0,0,0,0,0,0,0,0,0,78
%N A127773 Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
%H A127773 Harvey P. Dale, <a href="/A127773/b127773.txt">Table of n, a(n) for n = 1..1000</a>
%e A127773 First few rows of the triangle are:
%e A127773   1;
%e A127773   0, 3;
%e A127773   0, 0, 6;
%e A127773   0, 0, 0, 10;
%e A127773   0, 0, 0, 0, 15;
%e A127773   ...
%t A127773 Flatten[Table[{(n(n+1))/2,Table[0,{n}]},{n,10}]]  (* _Harvey P. Dale_, Apr 03 2011 *)
%t A127773 Table[PadLeft[{n (n+1)/2},n,0],{n,10}]//Flatten (* _Harvey P. Dale_, Jan 18 2025 *)
%o A127773 (Python)
%o A127773 from sympy.ntheory.primetest import is_square
%o A127773 def A127773(n): return n if is_square((n<<3)+1) else 0 # _Chai Wah Wu_, Jun 09 2025
%Y A127773 Cf. A127648, A000217, A127774, A010054.
%K A127773 nonn,easy,tabl
%O A127773 1,3
%A A127773 _Gary W. Adamson_, Jan 28 2007