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
KEYWORD
AUTHOR
Kival Ngaokrajang, Aug 08 2014
EXTENSIONS
Edited. - Wolfdieter Lang, Dec 08 2014
STATUS
approved