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A085930 Triangle read by rows in which row n contains n smallest (> 0) numbers which when incremented by n yield a triangular number.

%I A085930 #20 Jun 01 2020 04:57:56
%S A085930 2,1,4,3,7,12,2,6,11,17,1,5,10,16,23,4,9,15,22,30,39,3,8,14,21,29,38,
%T A085930 48,2,7,13,20,28,37,47,58,1,6,12,19,27,36,46,57,69,5,11,18,26,35,45,
%U A085930 56,68,81,95,4,10,17,25,34,44,55,67,80,94,109,3,9,16,24,33,43,54,66,79,93,108,124
%N A085930 Triangle read by rows in which row n contains n smallest (> 0) numbers which when incremented by n yield a triangular number.
%C A085930 Row n contains n terms.
%H A085930 Gheorghe Coserea, <a href="/A085930/b085930.txt">Rows n = 1..201, flattened</a>
%F A085930 T(n, k) = A000217(k+A003056(n))-n. - _David Wasserman_, Feb 23 2004
%e A085930 For n = 4 we have row 4 with 2, 6, 11, 17 since 2 + 4 = 3*4/2, 6 + 4 = 4*5/2, 11 + 4 = 5*6/2, 17 + 4 = 6*7/2.
%e A085930 Triangle starts:
%e A085930 n\k  [1]   [2]   [3]   [4]   [5]   [6]   [7]   [8]   [9]   [10]  [11]
%e A085930 [1]  2;
%e A085930 [2]  1,    4;
%e A085930 [3]  3,    7,    12;
%e A085930 [4]  2,    6,    11,   17;
%e A085930 [5]  1,    5,    10,   16,   23;
%e A085930 [6]  4,    9,    15,   22,   30,   39;
%e A085930 [7]  3,    8,    14,   21,   29,   38    48;
%e A085930 [8]  2,    7,    13,   20,   28,   37,   47,   58;
%e A085930 [9]  1,    6,    12,   19,   27,   36,   46,   57,   69;
%e A085930 [10] 5,    11,   18,   26,   35,   45,   56,   68,   81,   95;
%e A085930 [11] 4,    10,   17,   25,   34,   44,   55,   67,   80,   94,   109;
%e A085930 [12] ...
%o A085930 (PARI)
%o A085930 t(n,k) = my(x = (sqrtint(1+8*n)-1)\2); (x+k)*(x+k+1)/2 - n;
%o A085930 concat(vector(12, n, vector(n, k, t(n,k))))  \\ _Gheorghe Coserea_, Mar 25 2016
%Y A085930 Cf. A000217.
%K A085930 easy,nonn,tabl
%O A085930 1,1
%A A085930 _Amarnath Murthy_ and _Jason Earls_, Jul 14 2003
%E A085930 Offset corrected by _Gheorghe Coserea_, Mar 25 2016