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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (9,-15,7).
Programs
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Magma
[7^n + 7*n: n in [0..30]];
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Magma
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]];
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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] -
PARI
a(n)=7^n+7*n \\ Charles R Greathouse IV, Apr 18 2013
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