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

1,2

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), ...

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).

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

Links

Table of n, a(n) for n=1..55.

Formula

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

Prog

(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

Crossrefs

Cf. A001614, A059722, A056220, A058331.

Sequence in context: A236208 A284884 A130568 * A284894 A020497 A023490

Adjacent sequences: A143800 A143801 A143802 * A143804 A143805 A143806

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 01 2008

Status

approved