A182466 a(n) = 3*a(n-1) - 2*a(n-2) with a(0)=32 and a(1)=80.

32, 80, 176, 368, 752, 1520, 3056, 6128, 12272, 24560, 49136, 98288, 196592, 393200, 786416, 1572848, 3145712, 6291440, 12582896, 25165808, 50331632, 100663280, 201326576, 402653168, 805306352, 1610612720, 3221225456, 6442450928, 12884901872, 25769803760, 51539607536

Offset

0,1

Comments

Number of vertices into building blocks of 3d objects with 8 vertices.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

a(n) = a(n-1)*2 + 16.

G.f.: 16*(2-x)/(2*x^2-3*x+1). - Harvey P. Dale, Aug 23 2012

From Elmo R. Oliveira, Dec 08 2025: (Start)

E.g.f.: 16*exp(x)*(3*exp(x) - 1).

a(n) = 16*A153893(n) = 8*A033484(n+1) = 2*A182461(n). (End)

Example

a(0) = 8+16+8 = 32.
a(1) = 8+16+32+16+8 = 80.
a(2) = 8+16+32+64+32+16+8 = 176.
a(3) = 8+16+32+64+128+64+32+16+8 = 368.

Mathematica

LinearRecurrence[{3, -2}, {32, 80}, 40] (* or *) Table[8(3*2^n-2), {n, 40}] (* Harvey P. Dale, Aug 23 2012 *)
CoefficientList[Series[-((16 (x - 2))/(2 x^2 - 3 x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 02 2014 *)

Crossrefs

Cf. A000045, A028399, A038578, A089143, A173033, A182461, A182462, A182464, A182465, A182467.

Cf. A033484, A153893, A182461.

Sequence in context: A362044 A086047 A209378 * A234133 A203447 A340701

Adjacent sequences: A182463 A182464 A182465 * A182467 A182468 A182469

Keyword

nonn,easy

Author

Odimar Fabeny, Apr 30 2012

Status

approved