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

1,2

Links

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A207831 A207826 A035312 * A285321 A253561 A354960

Adjacent sequences: A056227 A056228 A056229 * A056231 A056232 A056233

Keyword

nice,nonn,easy,tabl

Author

Jonas Wallgren, Jul 30, 2000.

Status

approved