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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.
8
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
OFFSET
1,2
COMMENTS
See illustration in links.
The corresponding triangle with column sums is found in A251630. - Wolfdieter Lang, Dec 09 2014
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
Diagonals: A081436, A059270, ...
Row sums: A037270.
Sequence in context: A318466 A324819 A217112 * A245602 A060924 A365100
KEYWORD
nonn,easy,tabl
AUTHOR
Kival Ngaokrajang, Aug 08 2014
EXTENSIONS
Edited. - Wolfdieter Lang, Dec 08 2014
STATUS
approved