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Triangle read by rows: to get n-th row, start with -4n and successively add 5, 7, 9, 11, 13, ... until reaching a square.
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%I #19 Nov 29 2023 06:58:44

%S 0,-4,1,-8,-3,4,-12,-7,0,9,-16,-11,-4,5,16,-20,-15,-8,1,12,25,-24,-19,

%T -12,-3,8,21,36,-28,-23,-16,-7,4,17,32,49,-32,-27,-20,-11,0,13,28,45,

%U 64,-36,-31,-24,-15,-4,9,24,41,60,81,-40,-35,-28,-19,-8,5,20,37,56,77,100,-44,-39,-32,-23,-12

%N Triangle read by rows: to get n-th row, start with -4n and successively add 5, 7, 9, 11, 13, ... until reaching a square.

%C Row n has n+1 entries.

%C T(n,k) = n^2-4*k, n, k > = 0 read by antidiagonals. T(n,k) is discriminant the quadratic equation x^2+n*x+k=0. - _Boris Putievskiy_, Jan 11 2013

%H Boris Putievskiy, <a href="/A145917/b145917.txt">Rows n = 1..140 of triangle, flattened</a>

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations (of) Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.

%F From _Boris Putievskiy_, Jan 11 2013: (Start)

%F a(n) = (A002260(n)-1)^2 - 4*(A004736(n)-1), n >0.

%F a(n) = (i-1)^2-4(j-1), n>0, where

%F i = n-t*(t+1)/2,

%F j = (t*t+3*t+4)/2-n,

%F t = floor((-1+sqrt(8*n-7))/2). (End)

%K tabl,sign

%O 0,2

%A Jared Ricks (jaredricks(AT)yahoo.com), Oct 24 2008