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A137688
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2^A003056: 2^n appears n+1 times.
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12
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1, 2, 2, 4, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 128, 128, 128, 256, 256, 256, 256, 256, 256, 256, 256, 256, 512, 512, 512, 512, 512, 512, 512, 512, 512, 512, 1024, 1024, 1024, 1024, 1024, 1024
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OFFSET
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0,2
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COMMENTS
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Viewed as a triangle, it is computed like Pascal's triangle, but with 2^n on the triangle edges. - T. D. Noe, Jul 31 2013
Oresme numbers O(n) = n/2^n are an autosequence of the first kind. The corresponding sequence of the second kind is 1/2^n. The difference table is
1 1/2 1/4 1/8 ...
-1/2 -1/4 -1/8 -1/16 ...
1/4 1/8 1/16 1/32 ...
-1/8 -1/16 -1/32 -1/64 ...
etc.
The denominators on the antidiagonals are a(n). (End)
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LINKS
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FORMULA
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Closed-form formula for arbitrary left and right borders of Pascal like triangle see A228196. - Boris Putievskiy, Aug 19 2013
Viewed as a triangle T(n,k) : T(n,k)=2*T(n-1,k)+2*T(n-1,k-1)-4*T(n-2,k-1), T(0,0)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Dec 26 2013
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EXAMPLE
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Triangle T(n,k) begins:
1
2, 2
4, 4, 4
8, 8, 8, 8
16, 16, 16, 16, 16
32, 32, 32, 32, 32, 32
64, 64, 64, 64, 64, 64, 64
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MAPLE
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MATHEMATICA
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t = {}; Do[r = {}; Do[If[k == 0||k == n, m = 2^n, m = t[[n, k]] + t[[n, k + 1]]]; r = AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 9}]; t = Flatten[t] (* Vincenzo Librandi, Aug 01 2013 *)
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PROG
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(PARI) A137688(n)= 1<<floor(sqrt(2*n+2)-.5)
(Haskell)
a137688 n = a137688_list !! n
a137688_list = concat $ zipWith ($) (map replicate [1..]) (map (2^) [0..])
(GAP) Flat(List([0..10], n->List([1..n+1], k->2^n))); # Muniru A Asiru, Oct 23 2018
(Python)
from math import isqrt
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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