A076738 Expansion of (1+2*x+6*x^2)/(1-9*x^3).

1, 2, 6, 9, 18, 54, 81, 162, 486, 729, 1458, 4374, 6561, 13122, 39366, 59049, 118098, 354294, 531441, 1062882, 3188646, 4782969, 9565938, 28697814, 43046721, 86093442, 258280326, 387420489, 774840978, 2324522934, 3486784401, 6973568802, 20920706406, 31381059609

Offset

0,2

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (0,0,9).

Formula

From Amiram Eldar, Jul 07 2026:

a(n) = c * 9^floor(n/3), where c = 1, 2 or 6 if n == 0, 1 or 2 (mod 3), respectively.

Sum_{n>=0} 1/a(n) = 15/8.

Sum_{n>=0} (-1)^n/a(n) = 3/5. (End)

Mathematica

CoefficientList[Series[(1 + 2*x + 6*x^2)/(1 - 9*x^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 25 2021 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 9}, {1, 2, 6}, 34] (* Amiram Eldar, Jul 07 2026 *)

Crossrefs

Sequence in context: A156190 A285446 A367464 * A291100 A361271 A082290

Adjacent sequences: A076735 A076736 A076737 * A076739 A076740 A076741

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Nov 11 2002

Status

approved