A083224 a(n) = (6*7^n + (-7)^n)/7.

1, 5, 49, 245, 2401, 12005, 117649, 588245, 5764801, 28824005, 282475249, 1412376245, 13841287201, 69206436005, 678223072849, 3391115364245, 33232930569601, 166164652848005, 1628413597910449, 8142067989552245, 79792266297612001, 398961331488060005, 3909821048582988049

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (0,49).

Formula

a(n) = (6*7^n + (-7)^n)/7.

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

E.g.f.: (6*exp(7*x) + exp(-7*x))/7.

From Amiram Eldar, Feb 15 2026: (Start)

Sum_{n>=0} 1/a(n) = 49/40.

Sum_{n>=0} (-1)^n/a(n) = 49/60. (End)

Mathematica

LinearRecurrence[{0, 49}, {1, 5}, 30] (* Harvey P. Dale, Oct 12 2018 *)

Prog

(Magma) [(6*7^n+(-7)^n)/7: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011

Crossrefs

Cf. A083223, A083225.

Sequence in context: A196326 A273385 A058927 * A352371 A201358 A242035

Adjacent sequences: A083221 A083222 A083223 * A083225 A083226 A083227

Keyword

easy,nonn

Author

Paul Barry, Apr 23 2003

Status

approved