A046934 Same rule as Aitken triangle (A011971) except a(0,0)=1, a(1,0)=0.

1, 0, 1, 1, 1, 2, 2, 3, 4, 6, 6, 8, 11, 15, 21, 21, 27, 35, 46, 61, 82, 82, 103, 130, 165, 211, 272, 354, 354, 436, 539, 669, 834, 1045, 1317, 1671, 1671, 2025, 2461, 3000, 3669, 4503, 5548, 6865, 8536, 8536, 10207, 12232, 14693, 17693, 21362, 25865, 31413, 38278, 46814

Offset: 0

Author

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

Keywords

• tabl
• easy
• nice
• nonn

Comments

First differences of A046935 = this triangle seen as flattened list without the initial term. - Reinhard Zumkeller, Nov 10 2013

Examples

			[0] [   1]
[1] [   0,     1]
[2] [   1,     1,     2]
[3] [   2,     3,     4,     6]
[4] [   6,     8,    11,    15,    21]
[5] [  21,    27,    35,    46,    61,    82]
[6] [  82,   103,   130,   165,   211,   272,   354]
[7] [ 354,   436,   539,   669,   834,  1045,  1317,  1671]
[8] [1671,  2025,  2461,  3000,  3669,  4503,  5548,  6865,  8536]
[9] [8536, 10207, 12232, 14693, 17693, 21362, 25865, 31413, 38278, 46814]
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Crossrefs

Borders give A032347 and A032346. Cf. A046935.

Programs

Haskell

a046934 n k = a046934_tabl !! n !! k
a046934_row n = a046934_tabl !! n
a046934_tabl = [1] : iterate (\row -> scanl (+) (last row) row) [0,1]
a046934_list = concat a046934_tabl
-- Reinhard Zumkeller, Nov 10 2013

Maple

alias(PS = ListTools:-PartialSums):
A046934Triangle := proc(len) local a, k, P, T; a := 0; P := [1]; T := [];
for k from 1 to len  do T := [op(T), P]; P := PS([a, op(P)]); a := P[-1] od;
ListTools:-Flatten(T) end: A046934Triangle(10);  # Peter Luschny, Mar 29 2022

Mathematica

a[0, 0] = 1; a[1, 0] = 0; 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, Oct 14 2013 *)