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A080962
5th binomial transform of the periodic sequence (1,6,1,1,6,1...).
4
1, 11, 86, 596, 3896, 24656, 153056, 938816, 5714816, 34616576, 209010176, 1259303936, 7576795136, 45544656896, 273603485696, 1642963091456, 9863147257856, 59200358383616, 355288049647616, 2132071895269376, 12793805761150976, 76768332125044736, 460631982982823936
OFFSET
0,2
FORMULA
a(n) = 6*a(n-1) + 5*4^(n-1).
a(n) = (7/2)*6^n - (5/2)*4^n.
G.f.: (1+x)/((1-4*x)*(1-6*x)). - Vincenzo Librandi, Aug 06 2013
E.g.f.: exp(4*x)*(7*exp(2*x) - 5). - Stefano Spezia, Jul 23 2024
MATHEMATICA
CoefficientList[Series[(1 + x) / ((1 - 4 x) (1 - 6 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{10, -24}, {1, 11}, 20] (* Harvey P. Dale, Sep 06 2016 *)
PROG
(Magma) [(7/2)*6^n-(5/2)*4^n: n in [0..25]]; // Vincenzo Librandi, Aug 06 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 03 2003
STATUS
approved