A046937 Triangle read by rows. Same rule as Aitken triangle (A011971) except T(0,0) = 1, T(1,0) = 2.

1, 2, 3, 3, 5, 8, 8, 11, 16, 24, 24, 32, 43, 59, 83, 83, 107, 139, 182, 241, 324, 324, 407, 514, 653, 835, 1076, 1400, 1400, 1724, 2131, 2645, 3298, 4133, 5209, 6609, 6609, 8009, 9733, 11864, 14509, 17807, 21940, 27149, 33758

Offset: 0

Author

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

Keywords

• tabl
• easy
• nice
• nonn

Examples

			Triangle starts:
[0] [   1]
[1] [   2,    3]
[2] [   3,    5,    8]
[3] [   8,   11,   16,    24]
[4] [  24,   32,   43,    59,    83]
[5] [  83,  107,  139,   182,   241,   324]
[6] [ 324,  407,  514,   653,   835,  1076,  1400]
[7] [1400, 1724, 2131,  2645,  3298,  4133,  5209,  6609]
[8] [6609, 8009, 9733, 11864, 14509, 17807, 21940, 27149, 33758]
		

Links

• Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened

Crossrefs

Borders give A038561.

Cf. A011971.

Programs

Haskell

a046937 n k = a046937_tabl !! n !! k
a046937_row n = a046937_tabl !! n
a046937_tabl = [1] : iterate (\row -> scanl (+) (last row) row) [2,3]
-- Reinhard Zumkeller, Jan 13 2013

Maple

# Compare the analogue algorithm for the Catalan triangle in A350584.
A046937Triangle := proc(len) local A, P, T, n; A := [2]; P := [1]; T := [[1]];
for n from 1 to len-1 do P := ListTools:-PartialSums([A[-1], op(P)]);
A := P; T := [op(T), P] od; T end:
A046937Triangle(9): ListTools:-Flatten(%); # Peter Luschny, Mar 27 2022

Mathematica

a[0, 0] = 1; a[1, 0] = 2; 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, Jun 06 2013 *)