A143804 Triangle read by rows, thrice the Connell numbers (A001614) - 2.

1, 4, 10, 13, 19, 25, 28, 34, 40, 46, 49, 55, 61, 67, 73, 76, 82, 88, 94, 100, 106, 109, 115, 121, 127, 133, 139, 145, 148, 154, 160, 166, 172, 178, 184, 190, 193, 199, 205, 211, 217, 223, 229, 235, 241, 244, 250, 256, 262, 268, 274, 280, 286, 292, 298

Offset: 1

Author

Gary W. Adamson, Sep 01 2008

Keywords

• nonn
• tabl

Comments

Right border of the triangle = A100536: (1, 10, 25, 46, 73,...).

Left border = A056107: (1, 4, 13, 28, 49,...).

Row sums = A005915: (1, 14, 57, 148, 305,...).

n-th row = (right border then going to the left): (n-th term of A100536 followed by (n-1) operations of (-6), (-6), (-6),... As a Connell-like triangle, odd row terms are in the subset 6n-5; even row terms are in the set 6n-2.

Row 3 = (13, 19, 25) beginning with A100536(3) = 25 at the right then following the trajectory (-6), (-6).

Using the modular rules, the triangle begins (1; 4, 10; 13, 19, 25;...) since 1 == 6n-5, while 4 is the next higher term in the set 6n-2, then 10 also in the set 6n-2, being an even row.

Examples

			First few rows of the triangle:
  1;
  4, 10;
  13, 19, 25;
  28, 34, 40, 46;
  49, 55, 61, 67, 73;
  76, 82, 88, 94, 100, 106;
  ...
		

Crossrefs

Cf. A001614, A100536, A056107, A005915.

Programs

Python

from math import isqrt
def A143804(n): return 3*((m:=n<<1)-(k:=isqrt(m))-int(m>=k*(k+1)+1))-2 # Chai Wah Wu, Aug 01 2022

Formula

a(n) = 3*A001614(n) - 2.