A344747 a(n) = (1/6)*(3^n + (-2)^n - 1).

0, 2, 3, 16, 35, 132, 343, 1136, 3195, 10012, 29183, 89256, 264355, 799892, 2386023, 7185376, 21501515, 64613772, 193622863, 581305496, 1743042675, 5230875652, 15689131703, 47074385616, 141209175835, 423655489532, 1270910544543, 3812843481736, 11438306748995

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Index entries for linear recurrences with constant coefficients, signature (2,5,-6).

Formula

G.f.: x*(2 - x)/((1 - x)*(1 + 2*x)*(1 - 3*x)). - Andrew Howroyd, Jun 15 2021

a(n) = A094554(n-1) + 2*A094556(n-1). - Greg Dresden, Jun 19 2021

Example

a(4) = (1/6)*(3^4 + (-2)^4 - 1) = (1/6)*(81+16-1) = 16.

Mathematica

LinearRecurrence[{2, 5, -6}, {0, 2, 3}, 30] (* Greg Dresden, Jun 19 2021 *)

Crossrefs

Potentially related to A094554, A094555, and A094556 (which have the same recurrence).

Sequence in context: A034383 A350025 A072684 * A073633 A012357 A012701

Adjacent sequences: A344744 A344745 A344746 * A344748 A344749 A344750

Keyword

nonn,easy

Author

Ryan Brooks, Jun 14 2021

Status

approved