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A053219 Reverse of triangle A053218, read by rows.

%I A053219 #27 Oct 27 2023 22:00:45
%S A053219 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,
%T A053219 24,13,7,576,320,176,96,52,28,15,8,1280,704,384,208,112,60,32,17,9,
%U A053219 2816,1536,832,448,240,128,68,36,19,10,6144,3328,1792,960,512,272,144,76,40
%N A053219 Reverse of triangle A053218, read by rows.
%C A053219 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).
%C A053219 Subtriangle of triangle in A062111. - _Philippe Deléham_, Nov 21 2011
%C A053219 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
%e A053219 Triangle begins:
%e A053219 1
%e A053219 3, 2
%e A053219 8, 5, 3
%e A053219 20, 12, 7, 4
%e A053219 48, 28, 16, 9, 5 ...
%t A053219 Map[Reverse,NestList[FoldList[Plus,#[[1]]+1,#]&,{1},10]]//Grid (* _Geoffrey Critzer_, Jun 27 2013 *)
%o A053219 (Sage)
%o A053219 def u():
%o A053219     for n in PositiveIntegers():
%o A053219         yield n
%o A053219 def bous_variant(f):
%o A053219     k = 0
%o A053219     am = next(f)
%o A053219     a = [am]
%o A053219     while True:
%o A053219         yield list(a)
%o A053219         am = next(f)
%o A053219         a.append(am)
%o A053219         for m in range(k,-1,-1):
%o A053219             am += a[m]
%o A053219             a[m] = am
%o A053219         k += 1
%o A053219 b = bous_variant(u())
%o A053219 [next(b) for _ in range(8)] # _Peter Luschny_, Oct 30 2014
%Y A053219 Cf. A053218 (reverse of this triangle), A053220 (center elements), A053221 (row sums), A001792, A045618, A062111.
%K A053219 nonn,tabl
%O A053219 1,2
%A A053219 _Asher Auel_, Jan 01 2000