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A114284 Riordan array ((1-3*x)/(1-x), x).

%I A114284 #26 Jul 29 2025 00:21:33
%S A114284 1,-2,1,-2,-2,1,-2,-2,-2,1,-2,-2,-2,-2,1,-2,-2,-2,-2,-2,1,-2,-2,-2,-2,
%T A114284 -2,-2,1,-2,-2,-2,-2,-2,-2,-2,1,-2,-2,-2,-2,-2,-2,-2,-2,1,-2,-2,-2,-2,
%U A114284 -2,-2,-2,-2,-2,1,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,1
%N A114284 Riordan array ((1-3*x)/(1-x), x).
%C A114284 Inverse of A114283. Row sums are 1-2n. Diagonal sums are A114285. Sequence array of 3*0^n-2.
%H A114284 Michael De Vlieger, <a href="/A114284/b114284.txt">Table of n, a(n) for n = 0..1000</a>
%H A114284 Ângela Mestre, José Agapito, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Mestre/mestre2.html">Square Matrices Generated by Sequences of Riordan Arrays</a>, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
%F A114284 T(n, k) = if(k<=n, 3*0^(n-k)-2, 0).
%F A114284 a(n) = -3*floor((1/2)*sqrt(8*n+1)-1/2)+3*floor((1/2)*sqrt(8*n+9)-1/2)-2. - _Jackson Xier_, Oct 07 2011
%e A114284 Triangle begins:
%e A114284   1;
%e A114284   -2,1;
%e A114284   -2,-2,1;
%e A114284   -2,-2,-2,1;
%e A114284   -2,-2,-2,-2,1;
%t A114284 Table[-2 - 3 Floor[1/2 (-1 + Sqrt[1 + 8 x])] + 3 Floor[1/2 (-1 + Sqrt[9 + 8 x])], {x, 0, 65}] (* _Jackson Xier_, Oct 07 2011 *)
%K A114284 easy,sign,tabl
%O A114284 0,2
%A A114284 _Paul Barry_, Nov 20 2005