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 A159913 a(n) = 2^(A000120(n)+1)-1, where A000120(n) = number of nonzero bits in n. 4
 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31, 63, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31, 63, 7, 15, 15, 31, 15, 31, 31, 63, 15, 31, 31, 63, 31, 63, 63, 127, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Essentially the same sequence as A117973 and A001316. The latter entry has much more information. - N. J. A. Sloane, Jun 05 2009 First differences of A159912; every other term of A038573. From Gary W. Adamson, Oct 16 2009: (Start) Equals Sierpinski's gasket, A047999; as an infinite lower triangular matrix * [1,2,2,2,...] as a vector. (End) a(n) is also the number of cells turned ON at n-th generation in the outward corner version of the Ulam-Warburton cellular automaton of A147562, and a(n) is also the number of Y-toothpicks added at n-th generation in the outward corner version of the Y-toothpick structure of A160120. - David Applegate and Omar E. Pol, Jan 24 2016 LINKS David Applegate, The movie version N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS FORMULA a(n) = 2^A000120(2n+1)-1 = A038573(2n+1) = 2*A038573(n)+1 = A159912(n+1) - A159912(n). a(n) = A160019(n,n). - Philippe Deléham, Nov 15 2011 a(n) = n - Sum_{k=0..n} (-1)^binomial(n, k). - Peter Luschny, Jan 14 2018 EXAMPLE From Michael De Vlieger, Jan 25 2016: (Start) The number n converted to binary, "0" represented by "." for better visibility of 1's, totaling the 1's and calculating the sequence: n    Binary   Total                         a(n) 0 -> .     ->     0, thus 2^(0+1)-1 =  2-1 =  1 1 -> 1     ->     1,   "  2^(1+1)-1 =  4-1 =  3 2 -> 1.    ->     1,   "  2^(1+1)-1 =  4-1 =  3 3 -> 11    ->     2,   "  2^(2+1)-1 =  8-1 =  7 4 -> 1..   ->     1,   "  2^(1+1)-1 =  4-1 =  3 5 -> 1.1   ->     2,   "  2^(2+1)-1 =  8-1 =  7 6 -> 11.   ->     2,   "  2^(2+1)-1 =  8-1 =  7 7 -> 111   ->     3,   "  2^(3+1)-1 = 16-1 = 15 8 -> 1...  ->     1,   "  2^(1+1)-1 =  4-1 =  3 9 -> 1..1  ->     2,   "  2^(2+1)-1 =  8-1 =  7 10-> 1.1.  ->     2,   "  2^(2+1)-1 =  8-1 =  7 (End) MATHEMATICA Table[2^(DigitCount[n, 2][[1]] + 1) - 1, {n, 0, 78}] (* or *) Table[2^(Total@ IntegerDigits[n, 2] + 1) - 1, {n, 0, 78}] (* Michael De Vlieger, Jan 25 2016 *) PROG (PARI) A159913(n)=2<

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Last modified January 22 18:45 EST 2019. Contains 319365 sequences. (Running on oeis4.)