A247327 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.

1, 4, 12, 9, 27, 45, 16, 48, 80, 112, 25, 75, 125, 175, 225, 36, 108, 180, 252, 324, 396, 49, 147, 245, 343, 441, 539, 637, 64, 192, 320, 448, 576, 704, 832, 960, 81, 243, 405, 567, 729, 891, 1053, 1215, 1377, 100, 300, 500, 700, 900, 1100, 1300, 1500, 1700, 1900, 121, 363

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..57.

Kival Ngaokrajang, Illustration of initial terms

Example

Triangle begins:
  1
  4   12
  9   27  45
  16  48  80 112
  25  75 125 175 225
  36 108 180 252 324 396
  49 147 245 343 441 539 637

Prog

(Small Basic)
For n=1 To 20
  For k=1 To n*n+(n-1)*(n-1) Step 2*n
    c=0
    For i=1 To n
      If i=1 Then
        a=k
      Else
        a=a+2
      EndIf
      c=c+a
    EndFor
    TextWindow.Write(c+", ")
  EndFor
EndFor
(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

Crossrefs

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

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

Rows sum: A000538.

Cf. A241016.

Sequence in context: A273172 A307853 A334768 * A348419 A238581 A063608

Adjacent sequences: A247324 A247325 A247326 * A247328 A247329 A247330

Keyword

nonn,tabl

Author

Kival Ngaokrajang, Sep 13 2014

Status

approved