A321358 a(n) = (2*4^n + 7)/3.

3, 5, 13, 45, 173, 685, 2733, 10925, 43693, 174765, 699053, 2796205, 11184813, 44739245, 178956973, 715827885, 2863311533, 11453246125, 45812984493, 183251937965, 733007751853, 2932031007405, 11728124029613, 46912496118445, 187649984473773, 750599937895085, 3002399751580333

Offset: 0

Author

Paul Curtz, Nov 07 2018

Keywords

• nonn
• easy

Comments

Difference table:

3, 5, 13, 45, 173, 685, 2733, ... (this sequence)

2, 8, 32, 128, 512, 2048, 8192, ... A004171

6, 24, 96, 384, 1536, 6144, 24576, ... A002023

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A010701, A010727, A020988, A083594, A002023, A004171, A155980, A171382, A193579.

Programs

Mathematica

a[n_]:= (2*4^n + 7)/3; Array[a, 20, 0] (* or *)
CoefficientList[Series[1/3 (7 E^x + 2 E^(4 x)), {x, 0, 20}], x]*Table[n!, {n, 0, 20}] (* Stefano Spezia, Nov 10 2018 *)

PARI

a(n) = (2*4^n + 7)/3; \\ Michel Marcus, Nov 08 2018

PARI

Vec((3 - 10*x) / ((1 - x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Nov 10 2018

Formula

O.g.f.: (3 - 10*x) / ((1 - x)*(1 - 4*x)). - Colin Barker, Nov 10 2018

E.g.f.: (1/3)*(7*exp(x) + 2*exp(4*x)). - Stefano Spezia, Nov 10 2018

a(n) = 5*a(n-1) - 4*a(n-2), a(0) = 3, a(1) = 5.

a(n) = 4*a(n-1) - 7, a(0) = 3.

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

a(n) = A171382(2*n) = A155980(2*n+2).

a(n) = A193579(n)/3.

a(n) = A007583(n) + 2 = A001045(2*n+1) + 2.

Extensions

More terms from Michel Marcus, Nov 08 2018