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

%I A143803 #13 May 04 2024 14:29:48
%S A143803 1,3,7,9,13,17,19,23,27,31,33,37,41,45,49,51,55,59,63,67,71,73,77,81,
%T A143803 85,89,93,97,99,103,107,111,115,119,123,127,129,133,137,141,145,149,
%U A143803 153,157,161,163,167,171,175,179,183,187,191,195,199
%N A143803 a(n) = 2*A001614(n) - 1 where A001614 lists the Connell numbers.
%C A143803 Row sums = A059722: (1, 10, 39, 100, ...).
%C A143803 Right border of the triangle = A056220: (1, 7, 17, 31, 49, ...).
%C A143803 Left border = A058331: (1, 3, 9, 19, 33, 51, ...).
%C A143803 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.
%C A143803 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), ...
%C A143803 Row 3 = (9, 13, 17) since beginning with A056220(3) = 17 as rightmost term, we perform two operations of (-4), -(4)j.
%F A143803 a(n) = 2*A001614(n) - 1, where A001614 = the Connell numbers.
%e A143803 First few rows of the triangle =
%e A143803    1;
%e A143803    3,  7;
%e A143803    9, 13, 17;
%e A143803   19, 23, 27, 31;
%e A143803   33, 37, 41, 45, 49;
%e A143803   51, 55, 59, 63, 67, 71;
%e A143803   ...
%e A143803 Examples: a(5) = 13 = 2*A001614(5) - 1, where 7 = A001614(5).
%o A143803 (Python)
%o A143803 from math import isqrt
%o A143803 def A143803(n): return ((m:=n<<1)-(k:=isqrt(m))-int(m>=k*(k+1)+1)<<1)-1 # _Chai Wah Wu_, Aug 01 2022
%Y A143803 Cf. A001614, A059722, A056220, A058331.
%K A143803 nonn,tabl
%O A143803 1,2
%A A143803 _Gary W. Adamson_, Sep 01 2008