A046936 Same rule as Aitken triangle (A011971) except a(0,0)=0, a(1,0)=1.

0, 1, 1, 1, 2, 3, 3, 4, 6, 9, 9, 12, 16, 22, 31, 31, 40, 52, 68, 90, 121, 121, 152, 192, 244, 312, 402, 523, 523, 644, 796, 988, 1232, 1544, 1946, 2469, 2469, 2992, 3636, 4432, 5420, 6652, 8196, 10142, 12611, 12611, 15080, 18072, 21708, 26140

Offset: 0

Author

N. J. A. Sloane, R. K. Guy

Keywords

• tabl
• easy
• nice
• nonn

Examples

			Triangle starts:
0,
1, 1,
1, 2, 3,
3, 4, 6, 9,
9, 12, 16, 22, 31,
31, 40, 52, 68, 90, 121,
121, 152, 192, 244, 312, 402, 523,
523, 644, 796, 988, 1232, 1544, 1946, 2469,
2469, 2992, 3636, 4432, 5420, 6652, 8196, 10142, 12611,
12611, 15080, ...
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
• R. K. Guy, Letters to N. J. A. Sloane, June-August 1968
• Don Knuth, Email to N. J. A. Sloane, Jan 29 2018

Crossrefs

Borders give A040027. Reading across rows gives A007604.

Cf. A121207, A298804.

Programs

Haskell

a046936 n k = a046936_tabl !! n !! k
a046936_row n = a046936_tabl !! n
a046936_tabl = [0] : iterate (\row -> scanl (+) (last row) row) [1,1]
-- Reinhard Zumkeller, Jan 01 2014

Mathematica

a[0, 0] = 0; a[1, 0] = 1; a[n_, 0] := a[n, 0] = a[n-1, n-1]; a[n_, k_] := a[n, k] = a[n, k-1] + a[n-1, k-1]; Table[a[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 15 2013 *)

Python

from itertools import accumulate
def A046936(): # Compare function Gould_diag in A121207.
    yield [0]
    accu = [1, 1]
    while True:
        yield accu
        accu = list(accumulate([accu[-1]] + accu))
g = A046936()
[next(g) for  in range(9)] # _Peter Luschny, Apr 25 2016