

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
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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, n1 losses. For the case with exactly one loss, n1 wins, see A165900.  Max Winnick, Jun 28 2022


LINKS

Table of n, a(n) for n=0..31.
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), 816.
D. P. Roselle, Permutations by number of rises and successions, Proc. Amer. Math. Soc., 19 (1968), 816. [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(n1)  5*a(n2) + 2*a(n3).
G.f.: x*(13*x)/((1x)^2*(12*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



