A221909 a(n) = 7^n + 7*n.

1, 14, 63, 364, 2429, 16842, 117691, 823592, 5764857, 40353670, 282475319, 1977326820, 13841287285, 96889010498, 678223072947, 4747561510048, 33232930569713, 232630513987326, 1628413597910575, 11398895185373276, 79792266297612141, 558545864083284154, 3909821048582988203

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (9,-15,7).

Formula

G.f.: (1+5*x-48*x^2)/((1-x)^2*(1-7*x)).

a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3).

a(n) = A176972(n) - 1.

E.g.f.: exp(x)*(exp(6*x) + 7*x). - Elmo R. Oliveira, Sep 10 2024

Mathematica

Table[(7^n + 7 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 5 x - 48 x^2)/((1 - x)^2 (1 - 7 x)), {x, 0, 30}], x]

Prog

(Magma) [7^n + 7*n: n in [0..30]]; /* or */ I:=[1, 14, 63]; [n le 3 select I[n] else 9*Self(n-1)-15*Self(n-2)+7*Self(n-3): n in [1..30]];
(PARI) a(n)=7^n+7*n \\ Charles R Greathouse IV, Apr 18 2013

Crossrefs

Cf. A176972, A198397.

Sequence in context: A255499 A229739 A339136 * A229738 A239856 A214483

Adjacent sequences: A221906 A221907 A221908 * A221910 A221911 A221912

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2013

Status

approved