A215630 Triangle read by rows: T(n,k) = n^2 - n*k + k^2, 1 <= k <= n.

1, 3, 4, 7, 7, 9, 13, 12, 13, 16, 21, 19, 19, 21, 25, 31, 28, 27, 28, 31, 36, 43, 39, 37, 37, 39, 43, 49, 57, 52, 49, 48, 49, 52, 57, 64, 73, 67, 63, 61, 61, 63, 67, 73, 81, 91, 84, 79, 76, 75, 76, 79, 84, 91, 100, 111, 103, 97, 93, 91, 91, 93, 97, 103, 111

Offset: 1

Author

Reinhard Zumkeller, Nov 11 2012

Keywords

• nonn
• tabl

Comments

T(n,k) = A093995(n,k) - A075362(n,k) + A133819(n,k) = 2*A070216(n,k) - A215631(n,k), 1 <= k <= n.

Examples

			The triangle begins:
.  1:     1
.  2:     3    4
.  3:     7    7    9
.  4:    13   12   13   16
.  5:    21   19   19   21   25
.  6:    31   28   27   28   31   36
.  7:    43   39   37   37   39   43   49
.  8:    57   52   49   48   49   52   57   64
.  9:    73   67   63   61   61   63   67   73   81
. 10:    91   84   79   76   75   76   79   84   91  100
. 11:   111  103   97   93   91   91   93   97  103  111  121
. 12:   133  124  117  112  109  108  109  112  117  124  133  144 .
		

Links

• Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

Crossrefs

Cf. A004068 (row sums), A002061 (left edge), A000290 (right edge).

Cf. A003215 (central terms).

Programs

Haskell

a215630 n k = a215630_tabl !! (n-1) !! (k-1)
a215630_row n = a215630_tabl !! (n-1)
a215630_tabl = zipWith3 (zipWith3 (\u v w -> u - v + w))
                        a093995_tabl a075362_tabl a133819_tabl