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 A070313 a(n) = 2^n - (2*n+1). 9
 0, -1, -1, 1, 7, 21, 51, 113, 239, 493, 1003, 2025, 4071, 8165, 16355, 32737, 65503, 131037, 262107, 524249, 1048535, 2097109, 4194259, 8388561, 16777167, 33554381, 67108811, 134217673, 268435399, 536870853, 1073741763, 2147483585 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Binomial transform of (-1)^n! + !n. - Paul Barry, May 13 2004 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 Primes appear at positions n = 4, 7, 8, 28, 32, 81, 669, 1108, ... (A344781). - R. J. Mathar, Jan 22 2013 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 LINKS Denis Krotov, A partition of the hypercube into cosets of maximally nonparallel Hamming codes, arXiv:1210.0010v1 [cs.IT], Sep 28, 2012. D. P. Roselle, Permutations by number of rises and successions, Proc. Amer. Math. Soc., 19 (1968), 8-16. D. P. Roselle, Permutations by number of rises and successions, Proc. Amer. Math. Soc., 19 (1968), 8-16. [Annotated scanned copy] Index entries for linear recurrences with constant coefficients, signature (4,-5,2). FORMULA E.g.f.: (exp(x))^2 - exp(x) - 2*x*exp(x). - Paul Barry, May 13 2004 From Colin Barker, Mar 21 2012: (Start) a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). G.f.: -x*(1-3*x)/((1-x)^2*(1-2*x)). (End) MATHEMATICA lst={}; s=-1; Do[s+=s+n; AppendTo[lst, s], {n, 1, 5!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 18 2008 *) PROG (Maxima) makelist(2^n - (2*n+1), n, 0, 20); /* Martin Ettl, Jan 25 2013 */ (PARI) a(n)=2^n-(2*n+1) \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Second diagonal of A046739. Cf. A344781. Sequence in context: A146613 A083012 A233329 * A146733 A146709 A146400 Adjacent sequences: A070310 A070311 A070312 * A070314 A070315 A070316 KEYWORD sign,easy AUTHOR N. J. A. Sloane, May 16 2002 STATUS approved

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Last modified December 7 01:51 EST 2022. Contains 358649 sequences. (Running on oeis4.)