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 A237444 Triangle read by rows, T(n,k) is difference of column sum and row sum of natural numbers filled in n x n square. 1
 0, 1, -1, 6, 0, -6, 18, 6, -6, -18, 40, 20, 0, -20, -40, 75, 45, 15, -15, -45, -75, 126, 84, 42, 0, -42, -84, -126, 196, 140, 84, 28, -28, -84, -140, -196, 288, 216, 144, 72, 0, -72, -144, -216, -288, 405, 315, 225, 135, 45, -45, -135, -225, -315, -405, 550, 440, 330, 220, 110, 0, -110, -220, -330, -440, -550, 726, 594, 462, 330, 198, 66, -66 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS See illustration in links for construction rule. Column 1 = A002411. Column 2 = A005564 ,for n >= 3. Column 3 first differences = A140091. Nonnegative numbers of this sequence are given by A082375(n,k)*A000217(n), (see example). - Philippe Deléham, Feb 08 2014 LINKS Kival Ngaokrajang, Illustration for n = 1..5 FORMULA T(n,k) = - T(n,n-k+1), T(2n+1,n+1)= 0. - Philippe Deléham, Feb 08 2014 T(n+1,k+1) = A114327(n,k)*A000217(n). - Philippe Deléham, Feb 08 2014 EXAMPLE Triangle begins: n/k   1   2   3   4  5    6   7    8    9   ... 1   0 2   1  -1 3   6   0  -6 4  18   6  -6  18 5  40  20   0 -20 -40 6  75  45  15 -15 -45 -75 7 126  84  42   0 -42 -84 -126 8 196 140  84  28 -28 -84 -140 -196 9 288 216 144  72   0 -72 -144 -216 -288  ... ... A082375 begins: 0; 1; 2, 0; 3, 1; 4, 2, 0; 5, 3, 1; 6, 4, 2, 0; 7, 5, 3, 1; 8, 6, 4, 2, 0; 9, 7, 5, 3, 1; ..... A000217 (triangular numbers) begins: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, ... A082375(n,k)*A000217(n) begins: 0; 1; 6, 0; 18, 6; 40, 20, 0; 75, 45, 15; 126, 84, 42, 0; 196, 140, 84, 28; 288, 216, 144, 72, 0; 405, 315, 225, 135, 45; ... - Philippe Deléham, Feb 08 2014 PROG (Small Basic) For n = 1 to 20 For n1 = 1 To n c = 0 r = 0   For n2 = 1+n*(n1-1) To n+n*(n1-1)     c = c + n2   Endfor   For n3 = n1 To n1+n*(n-1) Step n     r = r + n3   EndFor a = r - c TextWindow.Write(a+", ") EndFor EndFor CROSSREFS Cf. A000217, A002411, A005564, A114327, A140091. Sequence in context: A165071 A341483 A223033 * A222918 A280480 A223104 Adjacent sequences:  A237441 A237442 A237443 * A237445 A237446 A237447 KEYWORD sign,tabl AUTHOR Kival Ngaokrajang, Feb 08 2014 STATUS approved

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Last modified January 28 04:01 EST 2022. Contains 350654 sequences. (Running on oeis4.)