%I A036563
%S A036563 2,1,1,5,13,29,61,125,253,509,1021,2045,4093,8189,16381,32765,65533,
%T A036563 131069,262141,524285,1048573,2097149,4194301,8388605,16777213,
%U A036563 33554429,67108861,134217725,268435453,536870909,1073741821,2147483645
%V A036563 -2,-1,1,5,13,29,61,125,253,509,1021,2045,4093,8189,16381,32765,65533,
%W A036563 131069,262141,524285,1048573,2097149,4194301,8388605,16777213,
%X A036563 33554429,67108861,134217725,268435453,536870909,1073741821,2147483645
%N A036563 2^n-3.
%C A036563 a(n+1) is the n-th number with exactly n 1's in binary representation. 
               - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 06 2003
%C A036563 Berstein and Onn: "For every m = 3k+1, the Graver complexity of the vertex-edge 
               incidence matrix of the complete bipirtite graph K(3,m) satisfies 
               g(m) >= 2^(k+2)-3." - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Sep 15 2007
%C A036563 Row sums of triangle A135857. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Dec 01 2007
%C A036563 a(n) = A164874(n-1,n-2) for n>2. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 29 2009]
%H A036563 Yael Berstein, Shmuel Onn, <a href="http://arXiv.org/pdf/0709.1500">The 
               Graver Complexity of Integer Programming</a>.
%F A036563 a(n)=2*a(n-1)+3
%F A036563 The sequence 1, 5, 13, ... has a(n)=4*2^n-3. These are the partial sums 
               of A046055. - Paul Barry (pbarry(AT)wit.ie), Aug 25 2003
%F A036563 Row sums of triangle A130459 starting (1, 5, 13, 29, 61,...). - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), May 26 2007
%F A036563 Row sums of triangle A131112 - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jun 15 2007
%F A036563 Binomial transform of [1, 4, 4, 4,...] = (1, 5, 13, 29, 61...). - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Sep 20 2007
%F A036563 a(n) = 2*StirlingS2(n,2) - 1, for n > 0. - Ross La Haye (rlahaye(AT)new.rr.com), 
               Jul 05 2008
%F A036563 a(n) = A000079(n)-3. [From Omar E. Pol (info(AT)polprimos.com), Dec 21 
               2008]
%F A036563 G.f.: 1/(1-2*x)-3/(1-x). E.g.f.: e^(2*x)-3*e^x. [From Mohammad K. Azarian 
               (azarian(AT)evansville.edu), Jan 14 2009]
%t A036563 a=1; lst={a}; k=4; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst 
               [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 15 2008]
%o A036563 (Other) sage: [gaussian_binomial(n,1,2)-2 for n in xrange(0,32)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2009]
%Y A036563 Row sums of triangular array A027960. A column of A119725.
%Y A036563 a(n) = A118654(n-3, 6), for n > 2.
%Y A036563 Cf. A081118, A130459, A131112.
%Y A036563 Cf. A050414, A050415.
%Y A036563 Cf. A135857.
%Y A036563 cF. A000079. [From Omar E. Pol (info(AT)polprimos.com), Dec 21 2008]
%Y A036563 Sequence in context: A024462 A049252 A098315 this_sequence A025264 A139622 
               A152656
%Y A036563 Adjacent sequences: A036560 A036561 A036562 this_sequence A036564 A036565 
               A036566
%K A036563 sign
%O A036563 0,1
%A A036563 N. J. A. Sloane (njas(AT)research.att.com).