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

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, 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, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78

Offset: 1

Author

Gary W. Adamson, Jan 28 2007

Keywords

• nonn
• easy
• tabl

Examples

			First few rows of the triangle are:
  1;
  0, 3;
  0, 0, 6;
  0, 0, 0, 10;
  0, 0, 0, 0, 15;
  ...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A127648, A000217, A127774, A010054.

Programs

Mathematica

Flatten[Table[{(n(n+1))/2,Table[0,{n}]},{n,10}]]  (* Harvey P. Dale, Apr 03 2011 *)
Table[PadLeft[{n (n+1)/2},n,0],{n,10}]//Flatten (* Harvey P. Dale, Jan 18 2025 *)

Python

from sympy.ntheory.primetest import is_square
def A127773(n): return n if is_square((n<<3)+1) else 0 # Chai Wah Wu, Jun 09 2025