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

1,2

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

Links

Table of n, a(n) for n=1..64.

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A211164 A097018 A127541 * A173030 A271589 A083087

Adjacent sequences: A053216 A053217 A053218 * A053220 A053221 A053222

Keyword

nonn,tabl

Author

Asher Auel, Jan 01 2000

Status

approved