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

%I A143804 #10 May 04 2024 14:29:51
%S A143804 1,4,10,13,19,25,28,34,40,46,49,55,61,67,73,76,82,88,94,100,106,109,
%T A143804 115,121,127,133,139,145,148,154,160,166,172,178,184,190,193,199,205,
%U A143804 211,217,223,229,235,241,244,250,256,262,268,274,280,286,292,298
%N A143804 Triangle read by rows, thrice the Connell numbers (A001614) - 2.
%C A143804 Right border of the triangle = A100536: (1, 10, 25, 46, 73,...).
%C A143804 Left border = A056107: (1, 4, 13, 28, 49,...).
%C A143804 Row sums = A005915: (1, 14, 57, 148, 305,...).
%C A143804 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.
%C A143804 Row 3 = (13, 19, 25) beginning with A100536(3) = 25 at the right then following the trajectory (-6), (-6).
%C A143804 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.
%F A143804 a(n) = 3*A001614(n) - 2.
%e A143804 First few rows of the triangle:
%e A143804   1;
%e A143804   4, 10;
%e A143804   13, 19, 25;
%e A143804   28, 34, 40, 46;
%e A143804   49, 55, 61, 67, 73;
%e A143804   76, 82, 88, 94, 100, 106;
%e A143804   ...
%o A143804 (Python)
%o A143804 from math import isqrt
%o A143804 def A143804(n): return 3*((m:=n<<1)-(k:=isqrt(m))-int(m>=k*(k+1)+1))-2 # _Chai Wah Wu_, Aug 01 2022
%Y A143804 Cf. A001614, A100536, A056107, A005915.
%K A143804 nonn,tabl
%O A143804 1,2
%A A143804 _Gary W. Adamson_, Sep 01 2008