A221907 a(n) = 5^n + 5*n.

1, 10, 35, 140, 645, 3150, 15655, 78160, 390665, 1953170, 9765675, 48828180, 244140685, 1220703190, 6103515695, 30517578200, 152587890705, 762939453210, 3814697265715, 19073486328220, 95367431640725, 476837158203230, 2384185791015735, 11920928955078240, 59604644775390745

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

Formula

G.f.: (1+3*x-24*x^2)/((1-x)^2*(1-5*x)).

a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).

a(n) = A176916(n) - 1.

a(n) = 5*A362555(n) for n > 0. - Hugo Pfoertner, Mar 01 2024

E.g.f.: exp(x)*(exp(4*x) + 5*x). - Elmo R. Oliveira, Sep 10 2024

Mathematica

Table[(5^n + 5 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 3 x - 24 x^2)/((1 - x)^2 (1 - 5 x)), {x, 0, 30}], x]
LinearRecurrence[{7, -11, 5}, {1, 10, 35}, 30] (* Harvey P. Dale, Jul 23 2013 *)

Prog

(Magma) [5^n + 5*n: n in [0..30]]; /* or */ I:=[1, 10, 35]; [n le 3 select I[n] else 7*Self(n-1)-11*Self(n-2)+5*Self(n-3): n in [1..30]];
(PARI) a(n)=5^n+5*n \\ Charles R Greathouse IV, Apr 18 2013

Crossrefs

Cf. A107585, A176916, A362555, A370557.

Sequence in context: A048507 A240267 A359317 * A195269 A070755 A126995

Adjacent sequences: A221904 A221905 A221906 * A221908 A221909 A221910

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2013

Status

approved