A392084 a(n) = 3*a(n-1) + 2*3^n - 1, a(0) = 0.

0, 5, 32, 149, 608, 2309, 8384, 29525, 101696, 344453, 1151456, 3808661, 12488864, 40655237, 131531648, 423292757, 1355971712, 4326195461, 13753427360, 43584805013, 137727983840, 434104657925, 1365076092992, 4283514636629, 13415402982848, 41940786167429

Offset

0,2

Comments

A recurrence relation that occurs in A391959.

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (7,-15,9).

Formula

a(n) = A391959(3^n).

From Stefano Spezia, Dec 31 2025: (Start)

a(n) = (3^n*(4*n - 1) + 1)/2.

G.f.: x*(5 - 3*x)/((1 - 3*x)^2*(1 - x)).

E.g.f.: exp(x)*(1 + exp(2*x)*(12*x - 1))/2. (End)

Mathematica

LinearRecurrence[{7, -15, 9}, {0, 5, 32}, 26] (* Amiram Eldar, Dec 31 2025 *)

Prog

(Python)
def A392084(n):
    if n == 0: return 0
    else: return 3*A392084(n-1) + 2*3**n - 1

Crossrefs

Cf. A391959.

Sequence in context: A359522 A001589 A271903 * A177467 A268153 A271153

Adjacent sequences: A392081 A392082 A392083 * A392085 A392086 A392087

Keyword

nonn,easy

Author

A.H.M. Smeets, Dec 30 2025

Status

approved