A083223 a(n) = (5*6^n+(-6)^n)/6.
1, 4, 36, 144, 1296, 5184, 46656, 186624, 1679616, 6718464, 60466176, 241864704, 2176782336, 8707129344, 78364164096, 313456656384, 2821109907456, 11284439629824, 101559956668416, 406239826673664, 3656158440062976
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (0,36).
Programs
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Magma
[(5*6^n+(-6)^n)/6: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011
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Mathematica
CoefficientList[Series[(1+4x)/((1+6x)(1-6x)),{x,0,50}],x] (* Harvey P. Dale, Mar 01 2011 *)
Formula
a(n) = (5*6^n+(-6)^n)/6.
G.f.: (1+4*x)/((1+6*x)*(1-6*x)).
E.g.f.: (5*exp(6*x)+exp(-6*x))/6.
a(n) = 36*a(n-2). - Wesley Ivan Hurt, Jun 24 2021