A155617 a(n) = 6^n + 4^n - 1.
1, 9, 51, 279, 1551, 8799, 50751, 296319, 1745151, 10339839, 61514751, 366991359, 2193559551, 13127802879, 78632599551, 471258726399, 2825404874751, 16943839313919, 101628676145151, 609634617917439, 3657257951690751
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (11,-34,24).
Crossrefs
Programs
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Magma
[6^n+4^n-1: n in [0..20]]; // Vincenzo Librandi, Feb 16 2013
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Magma
I:=[1,9,51]; [n le 3 select I[n] else 11*Self(n-1)-34*Self(n-2)+24*Self(n-3): n in [1..25]]; // Vincenzo Librandi, Feb 16 2013
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Mathematica
Table[(6^n + 4^n - 1^n), {n, 0, 30}] (* Vincenzo Librandi, Feb 16 2013 *) LinearRecurrence[{11,-34,24},{1,9,51},30] (* Harvey P. Dale, Mar 30 2019 *) -
PARI
a(n)=6^n+4^n-1 \\ Charles R Greathouse IV, Oct 16 2015
Formula
G.f.: 1/(1-6*x)+1/(1-4*x)-1/(1-x).
E.g.f.: exp(6*x) + exp(4*x) - exp(x).
a(n) = 10*a(n-1)-24*a(n-2) -15, n>1 - Gary Detlefs, Jun 21 2010
a(n) = 11*a(n-1)-34*a(n-2)+24*a(n-3). - Vincenzo Librandi, Feb 16 2013