A182467 a(n) = 3a(n-1) - 2a(n-2) with a(0)=36 and a(1)=90.

36, 90, 198, 414, 846, 1710, 3438, 6894, 13806, 27630, 55278, 110574, 221166, 442350, 884718, 1769454, 3538926, 7077870, 14155758, 28311534, 56623086, 113246190, 226492398, 452984814, 905969646, 1811939310, 3623878638, 7247757294, 14495514606, 28991029230

Offset: 0

Author

Odimar Fabeny, Apr 30 2012

Keywords

• nonn
• easy

Comments

Number of vertices into building blocks of 3d objects with 9 vertices.

Examples

			a(0) = 9+18+9;
a(1) = 9+18+36+18+9;
a(2) = 9+18+36+72+36+18+9;
a(3) = 9+18+36+72+144+72+36+18+9.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3, -2).

Crossrefs

Cf. A000045, A028399, A038578, A089143, A173033, A182461, A182462, A182464, A182465, A182466.

Programs

Mathematica

LinearRecurrence[{3,-2},{36,90},30] (* or *) CoefficientList[Series[(-18(x-2))/(1-3x+2x^2),{x,0,30}],x] (* Harvey P. Dale, Apr 29 2013 *)

Formula

a(n) = a(n-1)*2 + 18

G.f.: -((18*(x-2))/(2*x^2-3*x+1)). - Harvey P. Dale, Apr 29 2013

a(n) = 18*A153893(n). - Michel Marcus, Jun 01 2014