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A032125 "BIK" (reversible, indistinct, unlabeled) transform of 3,3,3,3... 3
3, 9, 30, 108, 408, 1584, 6240, 24768, 98688, 393984, 1574400, 6294528, 25171968, 100675584, 402677760, 1610661888, 6442549248, 25770000384, 103079608320, 412317646848, 1649269014528, 6597072912384, 26388285358080, 105553128849408 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of solutions (x,y,z) to x+y+z = 2^n, x>=0, y>=0, z>=0, gcd(x,y,z)=1. - Vladeta Jovovic, Dec 22 2002

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

C. G. Bower, Transforms (2)

Index entries for linear recurrences with constant coefficients, signature (6,-8)

FORMULA

a(n) = 3*2^(n-2)*(2^(n-1)+1). - Vladeta Jovovic, Dec 22 2002

Binomial transform of A067771 (if the offset is changed to 0). - Carl Najafi, Sep 09 2011

G.f. -3*x*(-1+3*x) / ( (4*x-1)*(2*x-1) ). a(n)=3*A007582(n-1). - R. J. Mathar, Sep 11 2011

a(1)=3, a(2)=9, a(n) = 6*a(n-1)-8*a(n-2). [Harvey P. Dale, Jan 01 2012]

E.g.f.: (3/8)*(exp(4*x) + 2*exp(2*x) - 3). - G. C. Greubel, Aug 22 2015

MATHEMATICA

Table[3*2^(n-2)(2^(n-1)+1), {n, 30}] (* or *) LinearRecurrence[{6, -8}, {3, 9}, 30] (* Harvey P. Dale, Jan 01 2012 *)

RecurrenceTable[{a[0]== 3, a[1]== 9, a[n]== 6*a[n-1]  - 8*a[n-2]}, a, {n, 50}] (* G. C. Greubel, Aug 22 2015 *)

CROSSREFS

a(n) = A048240(2^n).

Sequence in context: A128725 A099783 A200074 * A246472 A091699 A129167

Adjacent sequences:  A032122 A032123 A032124 * A032126 A032127 A032128

KEYWORD

nonn,easy

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 17 20:06 EST 2018. Contains 299296 sequences. (Running on oeis4.)