A168572 a(n) = Sum_{k=2..n}(7^k).

0, 49, 392, 2793, 19600, 137249, 960792, 6725593, 47079200, 329554449, 2306881192, 16148168393, 113037178800, 791260251649, 5538821761592, 38771752331193, 271402266318400, 1899815864228849, 13298711049601992, 93090977347213993

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (8,-7).

Formula

a(n) = 7^n + a(n-1), with a(1)=0.

From Robert Israel, Sep 24 2014: (Start)

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

G.f.: 49*x^2/((1-x)*(1-7*x)).

E.g.f.: 7*(exp(7*x) - 7*exp(x)+42)/6. (End)

a(n) = A104896(n) - 7. - Michel Marcus, Sep 25 2014

a(n) = 8*a(n-1) - 7*a(n-2). - G. C. Greubel, Jul 26 2016

Mathematica

RecurrenceTable[{a[1] == 0, a[n] == a[n-1] + 7^n}, a, {n, 30}] (* Vincenzo Librandi, Sep 24 2014 *)
LinearRecurrence[{8, -7}, {0, 49}, 25] (* G. C. Greubel, Jul 26 2016 *)
Join[{0}, Accumulate[7^Range[2, 20]]] (* Harvey P. Dale, Jul 29 2019 *)

Prog

(Magma) [n le 1 select (n-1) else Self(n-1) + 7^n: n in [1..30] ]; // Vincenzo Librandi, Sep 24 2014
(PARI) a(n)=7*(7^n - 7)/6 \\ Charles R Greathouse IV, Jul 26 2016

Crossrefs

Sequence in context: A206248 A100690 A157882 * A350382 A063874 A063132

Adjacent sequences: A168569 A168570 A168571 * A168573 A168574 A168575

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 30 2009

Extensions

Definition and examples simplified by Jon E. Schoenfield, Jun 19 2010

Status

approved