A253208 a(n) = 4^n + 3.

4, 7, 19, 67, 259, 1027, 4099, 16387, 65539, 262147, 1048579, 4194307, 16777219, 67108867, 268435459, 1073741827, 4294967299, 17179869187, 68719476739, 274877906947, 1099511627779, 4398046511107, 17592186044419, 70368744177667, 281474976710659

Offset: 0

Author

Vincenzo Librandi, Dec 29 2014

Keywords

• nonn
• easy

Comments

Subsequence of A226807.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A141725, A226807.

Cf. Numbers of the form k^n+k-1: A000057 (k=2), A168607 (k=3), this sequence (k=4), A242329 (k=5), A253209 (k=6), A253210 (k=7), A253211 (k=8), A253212 (k=9), A253213 (k=10).

Programs

Magma

[4^n+3: n in [0..30]];

Mathematica

Table[4^n + 3, {n, 0, 30}] (* or *) CoefficientList[Series[(4 - 13 x) / ((1 - x) (1 - 4 x)), {x, 0, 40}], x]

PARI

a(n)=4^n+3 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (4 - 13*x)/((1 - x)*(1 - 4*x)).

a(n) = 5*a(n-1) - 4*a(n-2) for n > 1.

From Elmo R. Oliveira, Nov 14 2023: (Start)

a(n) = 4*a(n-1) - 9 with a(0) = 4.

E.g.f.: exp(4*x) + 3*exp(x). (End)