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A173010 a(n) = round((2^n-n-1)/4). 1
0, 0, 1, 3, 7, 14, 30, 62, 126, 253, 509, 1021, 2045, 4092, 8188, 16380, 32764, 65531, 131067, 262139, 524283, 1048570, 2097146, 4194298, 8388602, 16777209, 33554425, 67108857, 134217721, 268435448, 536870904, 1073741816, 2147483640 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The variance v(n) = Sum_{k=0..2^n-n-1} (k-m(n))^2*p(n,k) of the distribution function p(n,k) := binomial(2^n-n-1, k)/2^(2^n-n-1) with m(n) its mean value is 0., 0.25, 1., 2.75, 6.5, 14.25, 30., 61.75, 125.5, 253.25, 509., 1020.75, 2044.5, 4092.25, 8188... We set a(n) = round(v(n)).

LINKS

Table of n, a(n) for n=1..33.

FORMULA

a(n) = round(-1/4+(1/4)*2^n-(1/4)*n).

G.f.: x^3*(1-x^3+x^4)/(1-3*x+2*x^2-2*x^6-x^4+3*x^5). [sign corrected by Georg Fischer, Apr 17 2020]

v(n) = (1/8)*2^n-1/4+v(-1+n) with v(1) = 0 and a(n) = round(v(n)).

MATHEMATICA

nn:=33; Rest[CoefficientList[Series[x^3*(1-x^3+x^4)/(1-3*x+2*x^2-2*x^6-x^4+3*x^5), {x, 0, nn}], x]] (* Georg Fischer, Apr 17 2020 *)

CROSSREFS

Cf. A173009.

Sequence in context: A066225 A305777 A139817 * A036892 A123707 A011947

Adjacent sequences:  A173007 A173008 A173009 * A173011 A173012 A173013

KEYWORD

nonn

AUTHOR

Thomas Wieder, Feb 07 2010

EXTENSIONS

Edited by Georg Fischer and Joerg Arndt, Apr 17 2020

STATUS

approved

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Last modified October 1 13:04 EDT 2020. Contains 337443 sequences. (Running on oeis4.)