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A053219 Reverse of triangle A053218, read by rows. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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 = f.next()

    a = [am]

    while True:

        yield list(a)

        am = f.next()

        a.append(am)

        for m in range(k, -1, -1):

            am += a[m]

            a[m] = am

        k += 1

b = bous_variant(u())

[b.next() 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 (asher.auel(AT)reed.edu), Jan 01 2000

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)