A155596 a(n) = 5^n - 2^n + 1^n.
1, 4, 22, 118, 610, 3094, 15562, 77998, 390370, 1952614, 9764602, 48826078, 244136530, 1220694934, 6103499242, 30517545358, 152587825090, 762939322054, 3814697003482, 19073485803838, 95367430592050, 476837156105974
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (8,-17,10).
Programs
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Mathematica
Table[5^n-2^n+1,{n,0,30}] (* or *) LinearRecurrence[{8,-17,10},{1,4,22},30] (* Harvey P. Dale, Sep 11 2019 *) -
PARI
a(n)=5^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015
Formula
G.f.: 1/(1-5*x)-1/(1-2*x)+1/(1-x).
E.g.f.: e^(5*x) - e^(2*x) + e^x.
a(n) = 7*a(n-1)-10*a(n-2)+4 with a(0)=1, a(1)=4. - Vincenzo Librandi, Jul 21 2010
a(n) = A005057(n)+1. - R. J. Mathar, Mar 10 2022