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 A241016 Triangle read by rows: T(n, k) = sum of k-th row of n X n square filled with the numbers 1 through n^2 reading across rows left-to-right. 7
 1, 3, 7, 6, 15, 24, 10, 26, 42, 58, 15, 40, 65, 90, 115, 21, 57, 93, 129, 165, 201, 28, 77, 126, 175, 224, 273, 322, 36, 100, 164, 228, 292, 356, 420, 484, 45, 126, 207, 288, 369, 450, 531, 612, 693, 55, 155, 255, 355, 455, 555, 655, 755, 855, 955, 66, 187, 308, 429, 550 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See illustration in links. The corresponding triangle with column sums is found in A251630. - Wolfdieter Lang, Dec 09 2014 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened Kival Ngaokrajang, Illustration of initial terms FORMULA T(n, k) = Sum_{j=1..n} (n*(k-1)+ j),  for n >= k >= 1. See the Michel Marcus program. - Wolfdieter Lang, Dec 08 2014 T(n, k) = binomial(n+1, 2) + n^2*(k-1). - Wolfdieter Lang, Dec 09 2014 EXAMPLE The triangle T(n, k) begins: n\k  1   2   3   4   5   6   7   8   9  10 ... 1:   1 2:   3   7 3:   6  15  24 4:  10  26  42  58 5:  15  40  65  90 115 6:  21  57  93 129 165 201 7:  28  77 126 175 224 273 322 8:  36 100 164 228 292 356 420 484 9:  45 126 207 288 369 450 531 612 693 10: 55 155 255 355 455 555 655 755 855 955 ... reformatted - Wolfdieter Lang, Dec 08 2014 MATHEMATICA Table[Sum[n*(k - 1) + j, {j, 1, n}], {n, 1, 10}, {k, 1, n}] // Flatten (* G. C. Greubel, Aug 23 2017 *) PROG (Small Basic) For n=1 To 20   For k=1 To n*n-(n-1) Step n     c=0     For i=1 To n       If i=1 Then         a=k       Else         a=a+1       EndIf       c=c+a     EndFor     TextWindow.Write(c+", ")   EndFor EndFor (PARI) trg(nn) = {for (n=1, nn, mm = matrix(n, n, i, j, j + n*(i-1)); for (i=1, n, print1(sum(j=1, n, mm[i, j]), ", "); ); print(); ); } \\ Michel Marcus, Sep 15 2014 CROSSREFS Columns k=1..6: A000217, A005449, A005475, A022265, A022267, A022269. Diagonals: A081436, A059270, ... Row sums: A037270. Sequence in context: A318466 A324819 A217112 * A245602 A060924 A213931 Adjacent sequences:  A241013 A241014 A241015 * A241017 A241018 A241019 KEYWORD nonn,easy,tabl AUTHOR Kival Ngaokrajang, Aug 08 2014 EXTENSIONS Edited. - Wolfdieter Lang, Dec 08 2014 STATUS approved

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Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)