A053219 Reverse of triangle A053218, read by rows.

1, 3, 2, 8, 5, 3, 20, 12, 7, 4, 48, 28, 16, 9, 5, 112, 64, 36, 20, 11, 6, 256, 144, 80, 44, 24, 13, 7, 576, 320, 176, 96, 52, 28, 15, 8, 1280, 704, 384, 208, 112, 60, 32, 17, 9, 2816, 1536, 832, 448, 240, 128, 68, 36, 19, 10, 6144, 3328, 1792, 960, 512, 272, 144, 76, 40

Offset: 1

Author

Asher Auel, Jan 01 2000

Keywords

• nonn
• tabl

Comments

First element in each row gives A001792. Difference between center element of row 2n-1 and row sum of row n (A053220(n+4) - A053221(n+4)) gives A045618(n).

Subtriangle of triangle in A062111. - Philippe Deléham, Nov 21 2011

Can be seen as the transform of 1, 2, 3, 4, 5, ... by a variant of the boustrophedon algorithm (see the Sage implementation). - Peter Luschny, Oct 30 2014

Examples

			Triangle begins:
1
3, 2
8, 5, 3
20, 12, 7, 4
48, 28, 16, 9, 5 ...
		

Crossrefs

Cf. A053218 (reverse of this triangle), A053220 (center elements), A053221 (row sums), A001792, A045618, A062111.

Programs

Mathematica

Map[Reverse,NestList[FoldList[Plus,#[[1]]+1,#]&,{1},10]]//Grid (* Geoffrey Critzer, Jun 27 2013 *)

Sage

def u():
    for n in PositiveIntegers():
        yield n
def bous_variant(f):
    k = 0
    am = next(f)
    a = [am]
    while True:
        yield list(a)
        am = next(f)
        a.append(am)
        for m in range(k,-1,-1):
            am += a[m]
            a[m] = am
        k += 1
b = bous_variant(u())
[next(b) for  in range(8)] # _Peter Luschny, Oct 30 2014