A081342 a(n) = (8^n + 2^n)/2.
1, 5, 34, 260, 2056, 16400, 131104, 1048640, 8388736, 67109120, 536871424, 4294968320, 34359740416, 274877911040, 2199023263744, 17592186060800, 140737488388096, 1125899906908160, 9007199254872064, 72057594038190080, 576460752303947776, 4611686018428436480
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (10,-16).
Programs
-
GAP
List([0..30], n-> (8^n + 2^n)/2); # G. C. Greubel, Jan 08 2020
-
Magma
[(8^n+2^n)/2: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
-
Maple
seq( (8^n + 2^n)/2, n=0..30); # G. C. Greubel, Jan 08 2020
-
Mathematica
Table[(8^n + 2^n)/2, {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *) -
PARI
a(n)=(8^n+2^n)/2 \\ Charles R Greathouse IV, Sep 28 2015
-
Sage
[(8^n + 2^n)/2 for n in (0..30)] # G. C. Greubel, Jan 08 2020
Formula
a(n) = (8^n + 2^n)/2.
a(n) = 10*a(n-1) - 16*a(n-2), a(0)=1, a(1)=5.
G.f.: (1-5*x)/((1-2*x)*(1-8*x)).
E.g.f.: exp(5*x)*cosh(3*x).
a(n) = ((5+sqrt(9))^n + (5-sqrt(9))^n)/2. - Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008
a(n) = A074603(n)/2. - Michel Marcus, Jan 09 2020
Comments