A193579 a(n) = 2*4^n + 7.

9, 15, 39, 135, 519, 2055, 8199, 32775, 131079, 524295, 2097159, 8388615, 33554439, 134217735, 536870919, 2147483655, 8589934599, 34359738375, 137438953479, 549755813895, 2199023255559, 8796093022215, 35184372088839, 140737488355335, 562949953421319, 2251799813685255

Offset: 0

Author

Brad Clardy, Sep 20 2011

Keywords

• nonn
• easy

Comments

Bisection of A168415 (odd part).

Links

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

Crossrefs

Cf. A168415, A020988.

Programs

Magma

[2*4^n + 7: n in [0..30]]; // Vincenzo Librandi, Sep 30 2011

Mathematica

2*4^Range[0,30]+7 (* or *) LinearRecurrence[{5,-4},{9,15},30] (* Harvey P. Dale, Jun 13 2020 *)

PARI

a(n) = 2*4^n+7 \\ Felix Fröhlich, Nov 07 2018

PARI

Vec(3*(3 - 10*x)/((1 - x)*(1 - 4*x)) + O(x^20)) \\ Felix Fröhlich, Nov 07 2018

Formula

a(n) = 2^(2n + 1) + 7 = 3*(A020988(n) + 3).

From Bruno Berselli, Sep 20 2011: (Start)

G.f.: 3*(3 - 10*x)/((1 - x)*(1 - 4*x)).

a(n) = A085688(A016969(n)). (End)

E.g.f.: 7*exp(x) + 2*exp(4*x). - Franck Maminirina Ramaharo, Nov 07 2018