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A046936 Same rule as Aitken triangle (A011971) except a(0,0)=0, a(1,0)=1. 7
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

EXAMPLE

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, ...

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-Fran├žois Alcover, Nov 15 2013 *)

PROG

(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

(Python 3)

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

CROSSREFS

Borders give A040027. Reading across rows gives A007604.

Cf. A121207, A298804.

Sequence in context: A228362 A155118 A091275 * A187067 A017831 A132289

Adjacent sequences:  A046933 A046934 A046935 * A046937 A046938 A046939

KEYWORD

tabl,easy,nice,nonn

AUTHOR

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

STATUS

approved

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Last modified March 20 05:29 EDT 2019. Contains 321344 sequences. (Running on oeis4.)