A081343 a(n) = (10^n + 4^n)/2.
1, 7, 58, 532, 5128, 50512, 502048, 5008192, 50032768, 500131072, 5000524288, 50002097152, 500008388608, 5000033554432, 50000134217728, 500000536870912, 5000002147483648, 50000008589934592, 500000034359738368
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (14,-40).
Crossrefs
Cf. A081342.
Programs
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GAP
List([0..25], n-> (10^n + 4^n)/2); # G. C. Greubel, Jan 07 2020
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Magma
[(10^n+4^n)/2: n in [0..25]]; // Vincenzo Librandi, Aug 08 2013
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Maple
seq( (10^n + 4^n)/2, n=0..25); # G. C. Greubel, Jan 07 2020
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Mathematica
CoefficientList[Series[(1-7x)/((1-4x)(1-10x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 08 2013 *) -
PARI
a(n)=(10^n+4^n)/2 \\ Charles R Greathouse IV, Oct 07 2015
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Sage
[(10^n + 4^n)/2 for n in (0..25)] # G. C. Greubel, Jan 07 2020
Formula
a(n) = 14*a(n-1) -40*a(n-2), a(0)=1, a(1)=7.
G.f.: (1-7*x)/((1-4*x)*(1-10*x)).
E.g.f.: exp(7*x) * cosh(3*x).
a(n) = ((7+sqrt(9))^n + (7-sqrt(9))^n)/2. - Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008
Comments