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

Author

Christian G. Bower

Keywords

• nonn
• easy

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)

Crossrefs

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

Programs

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 *)

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