A056230 Construct difference array so that (1) first row begins with 1, (2) every row is monotonic increasing, (3) no number appears more than once, (4) smallest number not yet used begins a new row. Sequence gives array read by antidiagonals.

1, 2, 3, 4, 6, 9, 7, 11, 17, 26, 12, 19, 30, 47, 73, 13, 25, 44, 74, 121, 194, 14, 27, 52, 96, 170, 291, 485, 15, 29, 56, 108, 204, 374, 665, 1150, 16, 31, 60, 116, 224, 428, 802, 1467, 2617, 18, 34, 65, 125, 241, 465, 893, 1695, 3162, 5779, 20, 38, 72, 137, 262

Offset: 1

Author

Jonas Wallgren, Jul 30 2000

Keywords

• nice
• nonn
• easy
• tabl

Examples

			Array begins
1 3 9 26 73 194 ...
.2 6 17 47 121 ...
. 4 11 30 74 ...
.. 7 19 44 ...
... 12 25 ...
.... 13 ...
		

Links

• Reinhard Zumkeller, Antidiagonals n=1..150 of array, flattened

Crossrefs

Cf. A057153 (first row), A200379 (second row), A052474 (main diagonal), A057154 (numbers not used), A056231, A056232, A056233, A056234.

Programs

Haskell

import Data.List (intersect, union, (\\))
a056230 n k = a056230_tabl !! (n-1) !! (k-1)
a056230_tabl = [1] : f [1] [2..] [1] where
   f adiag (a:as) us | null (adiag' `intersect` us) =
                       adiag' : f adiag' (as \\ adiag') (us `union` adiag')
                     | otherwise = f adiag as us
                     where adiag' = scanl (+) a adiag
-- Reinhard Zumkeller, Nov 19 2011