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A122746 G.f.: 1/((1-2*x)*(1-2*x^2)). 6
1, 2, 6, 12, 28, 56, 120, 240, 496, 992, 2016, 4032, 8128, 16256, 32640, 65280, 130816, 261632, 523776, 1047552, 2096128, 4192256, 8386560, 16773120, 33550336, 67100672, 134209536, 268419072, 536854528, 1073709056, 2147450880, 4294901760, 8589869056 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals row sums of triangle A156665 [From Gary W. Adamson, Feb 12 2009]

a(n) is the number of subsets of {1,2,...,n+1} that contain at least one odd integer. [From Geoffrey Critzer, Mar 03 2009]

REFERENCES

S. J. Cyvin et al., Theory of polypentagons, J. Chem. Inf. Comput. Sci., 33 (1993), 466-474.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-4).

FORMULA

a(2k) = A006516(k+1) = 2^k*(2^(k+1) - 1) = A020522(k+1) /2. a(2k+1) = 2*A006516(k+1) = 2^(k+1)*(2^(k+1) - 1) = A020522(k+1). - Alexander Adamchuk, Sep 25 2006

a(n)=2^(n+1)-2^(floor[(n+1)/2]) [From Geoffrey Critzer, Mar 03 2009]

a(n)=2*(a(n-1).bitwiseOR.a(n-2)),a(0)=1,a(1)=2 [Dec 12 2010]

G.f.: (1+x*Q(0))/(1-x)^2, where Q(k)= 1 - 1/(2^k - 2*x*2^(2*k)/(2*x*2^k - 1/(1 + 1/(2*2^k - 8*x*2^(2*k)/(4*x*2^k + 1/Q(k+1)))))); (continued fraction). - Sergei N. Gladkovskii, May 23 2013

a(0)=1, a(1)=2, a(2)=6, a(n)=2*a(n-1)+2*a(n-2)-4*a(n-3). - Harvey P. Dale, Jun 25 2013

MATHEMATICA

RecurrenceTable[{a[n] == 2 (BitOr[a[n - 1], a[n - 2]]), a[0] == 1, a[1] == 2}, a, {n, 0, 32}] (* Geoffrey Critzer, Jan 09 2011 *)

CoefficientList[Series[1/((1-2x)(1-2x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 2, -4}, {1, 2, 6}, 40] (* Harvey P. Dale, Jun 25 2013 *)

CROSSREFS

Essentially the same as A032085.

Cf. A006516, A020522.

A156665 [From Gary W. Adamson, Feb 12 2009]

Sequence in context: A112510 A011949 A089820 * A191394 A237500 A183467

Adjacent sequences:  A122743 A122744 A122745 * A122747 A122748 A122749

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 24 2006

STATUS

approved

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Last modified March 25 19:41 EDT 2017. Contains 284082 sequences.