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 A137688 2^A003056: 2^n appears n+1 times. 11
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First differences of A007664. 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 From Paul Curtz, Oct 23 2018: (Start) 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) LINKS Vincenzo Librandi, Rows n = 0..100, flattened FORMULA a(n) = 2^[sqrt(2n+2)-.5] = 2^A003056(n) = A007664(n+1) - A007664(n). 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 EXAMPLE 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 - Philippe Deléham, Dec 26 2013 MAPLE seq(seq(2^n, k=1..n+1), n=0..10); # Muniru A Asiru, Oct 23 2018 MATHEMATICA 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 *) PROG (PARI) A137688(n)= 1<List([1..n+1], k->2^n))); # Muniru A Asiru, Oct 23 2018 CROSSREFS Cf. A003056, A007664 (gives partial sums). Sequence in context: A320197 A124340 A071165 * A033720 A033728 A033744 Adjacent sequences:  A137685 A137686 A137687 * A137689 A137690 A137691 KEYWORD easy,nonn,tabl AUTHOR M. F. Hasler, Feb 06 2008 STATUS approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)