A228643 Triangle read by rows: T(n,1) = n * (n - 1) + 1 and for k: 1 < k <= n: T(n,k) = T(n,k-1) + T(n-1,k-1).

1, 3, 4, 7, 10, 14, 13, 20, 30, 44, 21, 34, 54, 84, 128, 31, 52, 86, 140, 224, 352, 43, 74, 126, 212, 352, 576, 928, 57, 100, 174, 300, 512, 864, 1440, 2368, 73, 130, 230, 404, 704, 1216, 2080, 3520, 5888, 91, 164, 294, 524, 928, 1632, 2848, 4928, 8448

Offset: 1

Author

J. M. Bergot and Reinhard Zumkeller, Aug 29 2013

Keywords

• nonn
• tabl

Comments

T(n,1) = A002061(n); T(n,2) = A005893(n-1) for n > 1;

T(n,n) = A007466(n).

Examples

			.   1:    1
.   2:    3,  4
.   3:    7, 10, 14
.   4:   13, 20, 30, 44
.   5:   21, 34, 54, 84, 128
.   6:   31, 52, 86,140, 224, 352
.   7:   43, 74,126,212, 352, 576, 928
.   8:   57,100,174,300, 512, 864,1440,2368
.   9:   73,130,230,404, 704,1216,2080,3520, 5888
.  10:   91,164,294,524, 928,1632,2848,4928, 8448,14336
.  11:  111,202,366,660,1184,2112,3744,6592,11520,19968,34304
.  12:  133,244,446,812,1472,2656,4768,8512,15104,26624,46592,80896.
		

Links

• Reinhard Zumkeller, Rows n = 1..100 of table, flattened

Programs

Haskell

a228643 n k = a228643_tabl !! (n-1) !! (k-1)
a228643_row n = a228643_tabl !! (n-1)
a228643_tabl = map fst $ iterate
   (\(row, x) -> (scanl (+) (x * (x - 1) + 1) row, x + 1)) ([1], 2)