A321003 a(n) = 2^n*(4*3^n-1).

3, 22, 140, 856, 5168, 31072, 186560, 1119616, 6718208, 40310272, 241863680, 1451186176, 8707125248, 52242767872, 313456640000, 1880739905536, 11284439564288, 67706637647872, 406239826411520, 2437438959517696, 14624633759203328, 87747802559414272

Offset

0,1

Comments

Conjectured to be the sum of A175046(i) for 1 <= i < 2^(n+1).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-12).

Formula

From Colin Barker, Nov 02 2018: (Start)

G.f.: (3 - 2*x) / ((1 - 2*x)*(1 - 6*x)).

a(n) = 8*a(n-1) - 12*a(n-2) for n>1.

(End)

E.g.f.: -exp(2*x)+4*exp(6*x). - Stefano Spezia, Nov 02 2018

Maple

a := n -> 2^n*(4*3^n-1):
seq(a(n), n = 0 .. 25); # Stefano Spezia, Nov 02 2018

Mathematica

a[n_]:=2^n*(4*3^n-1); Array[a, 25, 0] (* or *)
CoefficientList[Series[-E^(2 x) + 4 E^(6 x), {x, 0, 25}], x]*Table[k!, {k, 0, 25}] (* Stefano Spezia, Nov 02 2018 *)

Prog

(PARI) Vec((3 - 2*x) / ((1 - 2*x)*(1 - 6*x)) + O(x^25)) \\ Colin Barker, Nov 02 2018
(PARI) a(n) = 2^n*(4*3^n-1); \\ Michel Marcus, Nov 02 2018

Crossrefs

Cf. A175046, A171498, A321002.

Sequence in context: A033506 A091639 A091636 * A339227 A215051 A156089

Adjacent sequences: A321000 A321001 A321002 * A321004 A321005 A321006

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 01 2018

Status

approved