cp's OEIS Frontend

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.

%I A241016 #28 Aug 23 2017 16:06:21
%S A241016 1,3,7,6,15,24,10,26,42,58,15,40,65,90,115,21,57,93,129,165,201,28,77,
%T A241016 126,175,224,273,322,36,100,164,228,292,356,420,484,45,126,207,288,
%U A241016 369,450,531,612,693,55,155,255,355,455,555,655,755,855,955,66,187,308,429,550
%N 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.
%C A241016 See illustration in links.
%C A241016 The corresponding triangle with column sums is found in A251630. - _Wolfdieter Lang_, Dec 09 2014
%H A241016 G. C. Greubel, <a href="/A241016/b241016.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%H A241016 Kival Ngaokrajang, <a href="/A241016/a241016.pdf">Illustration of initial terms</a>
%F A241016 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
%F A241016 T(n, k) = binomial(n+1, 2) + n^2*(k-1). - _Wolfdieter Lang_, Dec 09 2014
%e A241016 The triangle T(n, k) begins:
%e A241016 n\k  1   2   3   4   5   6   7   8   9  10 ...
%e A241016 1:   1
%e A241016 2:   3   7
%e A241016 3:   6  15  24
%e A241016 4:  10  26  42  58
%e A241016 5:  15  40  65  90 115
%e A241016 6:  21  57  93 129 165 201
%e A241016 7:  28  77 126 175 224 273 322
%e A241016 8:  36 100 164 228 292 356 420 484
%e A241016 9:  45 126 207 288 369 450 531 612 693
%e A241016 10: 55 155 255 355 455 555 655 755 855 955
%e A241016 ... reformatted - _Wolfdieter Lang_, Dec 08 2014
%t A241016 Table[Sum[n*(k - 1) + j, {j,1,n}], {n,1,10}, {k,1,n}] // Flatten (* _G. C. Greubel_, Aug 23 2017 *)
%o A241016 (Small Basic)
%o A241016 For n=1 To 20
%o A241016   For k=1 To n*n-(n-1) Step n
%o A241016     c=0
%o A241016     For i=1 To n
%o A241016       If i=1 Then
%o A241016         a=k
%o A241016       Else
%o A241016         a=a+1
%o A241016       EndIf
%o A241016       c=c+a
%o A241016     EndFor
%o A241016     TextWindow.Write(c+", ")
%o A241016   EndFor
%o A241016 EndFor
%o A241016 (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
%Y A241016 Columns k=1..6: A000217, A005449, A005475, A022265, A022267, A022269.
%Y A241016 Diagonals: A081436, A059270, ...
%Y A241016 Row sums: A037270.
%K A241016 nonn,easy,tabl
%O A241016 1,2
%A A241016 _Kival Ngaokrajang_, Aug 08 2014
%E A241016 Edited. - _Wolfdieter Lang_, Dec 08 2014