A143803 a(n) = 2*A001614(n) - 1 where A001614 lists the Connell numbers.

1, 3, 7, 9, 13, 17, 19, 23, 27, 31, 33, 37, 41, 45, 49, 51, 55, 59, 63, 67, 71, 73, 77, 81, 85, 89, 93, 97, 99, 103, 107, 111, 115, 119, 123, 127, 129, 133, 137, 141, 145, 149, 153, 157, 161, 163, 167, 171, 175, 179, 183, 187, 191, 195, 199

Offset: 1

Author

Gary W. Adamson, Sep 01 2008

Keywords

• nonn
• tabl

Comments

Row sums = A059722: (1, 10, 39, 100, ...).

Right border of the triangle = A056220: (1, 7, 17, 31, 49, ...).

Left border = A058331: (1, 3, 9, 19, 33, 51, ...).

Connell-like triangle read by rows: odd rows are in the set 4n-3, evens are in 4n-1. Leftmost term in the next row is the next higher term consistent with the modular rule.

Given A056220: (1, 7, 17, 31, 49, 71, ...) as the rightmost diagonal; the triangle is generated starting from the right: (n-th term of A056220, then (n-1) operations of the trajectory (-4), (-4), (-4), ...

Row 3 = (9, 13, 17) since beginning with A056220(3) = 17 as rightmost term, we perform two operations of (-4), -(4)j.

Examples

			First few rows of the triangle =
   1;
   3,  7;
   9, 13, 17;
  19, 23, 27, 31;
  33, 37, 41, 45, 49;
  51, 55, 59, 63, 67, 71;
  ...
Examples: a(5) = 13 = 2*A001614(5) - 1, where 7 = A001614(5).
		

Crossrefs

Cf. A001614, A059722, A056220, A058331.

Programs

Python

from math import isqrt
def A143803(n): return ((m:=n<<1)-(k:=isqrt(m))-int(m>=k*(k+1)+1)<<1)-1 # Chai Wah Wu, Aug 01 2022

Formula

a(n) = 2*A001614(n) - 1, where A001614 = the Connell numbers.