A081493 Triangle T(n,k) read by rows in which the n-th row begins with T(n,1) = n and contains n terms of an arithmetic progression with a common difference of (n-1).

1, 2, 3, 3, 5, 7, 4, 7, 10, 13, 5, 9, 13, 17, 21, 6, 11, 16, 21, 26, 31, 7, 13, 19, 25, 31, 37, 43, 8, 15, 22, 29, 36, 43, 50, 57, 9, 17, 25, 33, 41, 49, 57, 65, 73, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101, 111, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133

Offset: 1

Author

Amarnath Murthy, Mar 25 2003

Keywords

• nonn
• tabl
• easy

Comments

n-th row sum gives the sum corresponding to the magic square of order n.

Examples

			Triangle T(n,k) begins:
  1;
  2,  3;
  3,  5,  7;
  4,  7, 10, 13;
  5,  9, 13, 17, 21;
  6, 11, 16, 21, 26, 31;
  ...
		

Links

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

Crossrefs

Row sums are A006003.

Central terms of rows give A001844.

Programs

Mathematica

Table[NestList[#+n-1&,n,n-1],{n,20}]//Flatten (* Harvey P. Dale, May 14 2023 *)

Formula

T(i,j) = i + (i-1)*(j-1). - David Wasserman, Jun 03 2004

Extensions

Corrected and extended by David Wasserman, Jun 03 2004