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A173009 Expansion of o.g.f. (x-x^2+x^3)/(2*x^4-3*x^3-x^2+3*x-1). 1
0, 1, 2, 6, 13, 29, 60, 124, 251, 507, 1018, 2042, 4089, 8185, 16376, 32760, 65527, 131063, 262134, 524278, 1048565, 2097141, 4194292, 8388596, 16777203, 33554419, 67108850, 134217714, 268435441, 536870897 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The mean value m(n) = sum(k*p(n,k), k = 0 .. 2^n-n-1) of the distribution function p(n,k) := binomial(2^n-n-1, k)/2^(2^n-n-1) is 0., 0.5, 2., 5.5, 13., 28.5, 60., 123.5, 251., 506.5, 1018., 2041.5, 4089., 8184.5... We set a(n) = round(m(n)).

The half-integer sequence h(n) = 0, 1/2, 2, 11/2, 13, 57/2, 60, 247/2, 251, 1013/2, 1018, 4083/2, 4089, 16369/2, 16376, 65519/2, 65527, ... is the BINOMIALi transform of 0, 1/2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

LINKS

Table of n, a(n) for n=1..30.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

FORMULA

h(n) = (1/2)*2^n-(1/2)*n-1/2.

G.f.: (x-x^2+x^3)/(2*x^4-3*x^3-x^2+3*x-1).

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

a(1)=0, a(2)=1, a(3)=2, a(4)=6, a(n) = 3*a(n-1)-a(n-2)-3*a(n-3)+ 2*a(n-4). - Harvey P. Dale, Nov 16 2011

MATHEMATICA

Join[{a=0, b=1}, Table[c=b+2*a+n; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 21 2011*)

Table[Ceiling[(2^n-n-1)/2], {n, 30}] (* or *) LinearRecurrence[{3, -1, -3, 2}, {0, 1, 2, 6}, 30] (* Harvey P. Dale, Nov 16 2011 *)

PROG

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 2, -3, -1, 3]^(n-1)*[0; 1; 2; 6])[1, 1] \\ Charles R Greathouse IV, Apr 18 2020

CROSSREFS

Cf. A173010, A016031, A000295.

Sequence in context: A289764 A289887 A055243 * A212586 A276411 A180965

Adjacent sequences:  A173006 A173007 A173008 * A173010 A173011 A173012

KEYWORD

nonn,easy

AUTHOR

Thomas Wieder, Feb 07 2010

STATUS

approved

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Last modified September 29 06:29 EDT 2020. Contains 337425 sequences. (Running on oeis4.)