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%I #10 Apr 18 2021 02:33:59
%S 1,5,3,15,11,6,34,27,19,10,65,54,42,29,15,111,95,78,60,41,21,175,153,
%T 130,106,81,55,28,260,231,201,170,138,105,71,36,369,332,294,255,215,
%U 174,132,89,45,505,459,412,364,315,265,214,162,109,55,671,615,558,500,441,381,320,258,195,131,66
%N Triangle read by rows: T(n,k) = (n^2 + k)*(n - k + 1)/2.
%H Andrew Howroyd, <a href="/A178067/b178067.txt">Table of n, a(n) for n = 1..1275</a> (rows 1..50)
%F As infinite lower triangular matrices, A000027 * A000012 (the all 1's triangle).
%e First few rows of the triangle:
%e 1;
%e 5, 3;
%e 15, 11, 6;
%e 34, 27, 19, 10;
%e 65, 54, 42, 29, 15;
%e 111, 95, 78, 60, 41, 21;
%e 175, 153, 130, 106, 81, 55, 28;
%e 260, 231, 201, 170, 138, 105, 71, 36;
%e 369, 332, 294, 255, 215, 174, 132, 89, 45;
%e 505, 459, 412, 364, 315, 265, 214, 162, 109, 55;
%e 671, 615, 558, 500, 441, 381, 320, 258, 195, 131, 66;
%e ...
%e Example: Row 3 = (15, 11 6) since row 3 of A000027 as a triangle = (4, 5, 6); then taking partial sums from the right.
%Y Column 1 is A006003.
%Y Row sums are A132117.
%Y Main diagonal is A000217.
%K nonn,tabl,easy
%O 1,2
%A _Gary W. Adamson_, May 18 2010
%E Name changed and terms a(37) and beyond from _Andrew Howroyd_, Apr 17 2021
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