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A145917 Triangle read by rows: to get n-th row, start with -4n and successively add 5, 7, 9, 11, 13, ... until reaching a square.

%I A145917 #26 Mar 22 2025 18:49:52
%S A145917 0,-4,1,-8,-3,4,-12,-7,0,9,-16,-11,-4,5,16,-20,-15,-8,1,12,25,-24,-19,
%T A145917 -12,-3,8,21,36,-28,-23,-16,-7,4,17,32,49,-32,-27,-20,-11,0,13,28,45,
%U A145917 64,-36,-31,-24,-15,-4,9,24,41,60,81,-40,-35,-28,-19,-8,5,20,37,56,77,100
%N A145917 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 A145917 Row n has n+1 entries.
%C A145917 T(n,k) is the discriminant of the quadratic equation x^2+n*x+k=0. - _Boris Putievskiy_, Jan 11 2013
%H A145917 Boris Putievskiy, <a href="/A145917/b145917.txt">Rows n = 1..140 of triangle, flattened</a>
%H A145917 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 A145917 From _Boris Putievskiy_, Jan 11 2013: (Start)
%F A145917 T(n,k) = n^2-4*k, n, k >= 0 array read by antidiagonals.
%F A145917 a(n) = (A002260(n)-1)^2 - 4*(A004736(n)-1), n >0.
%F A145917 a(n) = (i-1)^2-4(j-1), n>0, where i = n-t*(t+1)/2, j = (t*t+3*t+4)/2-n, and t = floor((-1+sqrt(8*n-7))/2). (End)
%e A145917 As a triangle:
%e A145917    0;
%e A145917   -4,   1;
%e A145917   -8,  -3,  4;
%e A145917  -12,  -7,  0, 9;
%e A145917  -16, -11, -4, 5, 16;
%e A145917  -20, -15, -8, 1, 12, 25;
%e A145917   ...
%e A145917 As an array:
%e A145917   0 -4 -8 -12 -16 -20 -24
%e A145917   1 -3 -7 -11 -15 -19 -23
%e A145917   4  0 -4  -8 -12 -16 -20
%e A145917   9  5  1  -3  -7 -11 -15
%e A145917  16 12  8   4   0  -4  -8
%e A145917  25 21 17  13   9   5   1
%e A145917  36 32 28  24  20  16  12
%K A145917 tabl,sign
%O A145917 0,2
%A A145917 Jared Ricks (jaredricks(AT)yahoo.com), Oct 24 2008