This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A070313 #51 Feb 13 2024 18:43:03
%S A070313 0,-1,-1,1,7,21,51,113,239,493,1003,2025,4071,8165,16355,32737,65503,
%T A070313 131037,262107,524249,1048535,2097109,4194259,8388561,16777167,
%U A070313 33554381,67108811,134217673,268435399,536870853,1073741763,2147483585
%N A070313 a(n) = 2^n - (2*n+1).
%C A070313 Binomial transform of (-1)^n! + !n. - _Paul Barry_, May 13 2004
%C A070313 This appears as the exponent in Krotov, who writes on p. 2: "in general, two extended Hamming codes can intersect in 2^(2^m - 2m - 1) elements." - _Jonathan Vos Post_, Jan 13 2013
%C A070313 Primes appear at positions n = 4, 7, 8, 28, 32, 81, 669, 1108, ... (A344781). - _R. J. Mathar_, Jan 22 2013
%C A070313 a(n) is the total number of dollars lost when using the Martingale method (bet $1, if win then continue to bet $1, if lose then double next bet) for n trials of a wager with exactly one win, n-1 losses. For the case with exactly one loss, n-1 wins, see A165900. - _Max Winnick_, Jun 28 2022
%H A070313 Denis Krotov, <a href="http://arxiv.org/abs/1210.0010">A partition of the hypercube into cosets of maximally nonparallel Hamming codes</a>, arXiv:1210.0010v1 [cs.IT], Sep 28, 2012.
%H A070313 D. P. Roselle, <a href="https://dx.doi.org/10.1090/S0002-9939-1968-0218256-9">Permutations by number of rises and successions</a>, Proc. Amer. Math. Soc., 19 (1968), 8-16.
%H A070313 D. P. Roselle, <a href="/A046739/a046739.pdf"> Permutations by number of rises and successions</a>, Proc. Amer. Math. Soc., 19 (1968), 8-16. [Annotated scanned copy]
%H A070313 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A070313 E.g.f.: (exp(x))^2 - exp(x) - 2*x*exp(x). - _Paul Barry_, May 13 2004
%F A070313 From _Colin Barker_, Mar 21 2012: (Start)
%F A070313 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
%F A070313 G.f.: -x*(1-3*x)/((1-x)^2*(1-2*x)). (End)
%t A070313 lst={};s=-1;Do[s+=s+n;AppendTo[lst, s], {n, 1, 5!, 2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 18 2008 *)
%t A070313 Table[2^n-(2n+1),{n,0,40}] (* _Harvey P. Dale_, Feb 13 2024 *)
%o A070313 (Maxima) makelist(2^n - (2*n+1),n,0,20); /* _Martin Ettl_, Jan 25 2013 */
%o A070313 (PARI) a(n)=2^n-(2*n+1) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A070313 Second diagonal of A046739.
%Y A070313 Cf. A344781.
%K A070313 sign,easy
%O A070313 0,5
%A A070313 _N. J. A. Sloane_, May 16 2002