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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (8,-7).
Programs
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Magma
[n le 1 select (n-1) else Self(n-1) + 7^n: n in [1..30] ]; // Vincenzo Librandi, Sep 24 2014
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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 *) -
PARI
a(n)=7*(7^n - 7)/6 \\ Charles R Greathouse IV, Jul 26 2016
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
Extensions
Definition and examples simplified by Jon E. Schoenfield, Jun 19 2010