A032125 "BIK" (reversible, indistinct, unlabeled) transform of 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

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