A080962 5th binomial transform of the periodic sequence (1,6,1,1,6,1...).

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

Author

Paul Barry, Mar 03 2003

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (10,-24).

Crossrefs

Cf. A080960, A080961, A081033.

Programs

Magma

[(7/2)*6^n-(5/2)*4^n: n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

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 *)

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