A247327 - OEIS

%I #12 Feb 27 2015 23:32:55

%S 1,4,12,9,27,45,16,48,80,112,25,75,125,175,225,36,108,180,252,324,396,

%T 49,147,245,343,441,539,637,64,192,320,448,576,704,832,960,81,243,405,

%U 567,729,891,1053,1215,1377,100,300,500,700,900,1100,1300,1500,1700,1900,121,363

%N Triangle read by rows: T(n,k) = sum of k-th row of n X n square filled with odd numbers 1 through 2*n^2-1 reading across rows left-to-right.

%C See illustration in links. Column c(k) = (2*k - 1)*n^2. Diagonal d(m) = (2*n - 2*m + 1)*n^2.

%H Kival Ngaokrajang, <a href="/A247327/a247327.pdf">Illustration of initial terms</a>

%e Triangle begins:

%e   1

%e   4   12

%e   9   27  45

%e   16  48  80 112

%e   25  75 125 175 225

%e   36 108 180 252 324 396

%e   49 147 245 343 441 539 637

%o (Small Basic)

%o For n=1 To 20

%o   For k=1 To n*n+(n-1)*(n-1) Step 2*n

%o     c=0

%o     For i=1 To n

%o       If i=1 Then

%o         a=k

%o       Else

%o         a=a+2

%o       EndIf

%o       c=c+a

%o     EndFor

%o     TextWindow.Write(c+", ")

%o   EndFor

%o EndFor

%o (PARI) trg(nn) = {for (n=1, nn, mm = matrix(n, n, i, j, (2*j-1) + (2*n)*(i-1)); for (i=1, n, print1(sum(j=1, n, mm[i, j]), ", ");); print(););} \\ _Michel Marcus_, Sep 15 2014

%Y Column: c(1) = A000290, c(2) = A033428, c(3) = A033429.

%Y Diagonal: d(1) = A015237, d(2) = A015238, d(3) = A015240.

%Y Rows sum: A000538.

%Y Cf. A241016.

%K nonn,tabl

%O 1,2

%A _Kival Ngaokrajang_, Sep 13 2014