A084171 Binomial transform of generalized Jacobsthal numbers A084170.
1, 3, 11, 37, 119, 373, 1151, 3517, 10679, 32293, 97391, 293197, 881639, 2649013, 7955231, 23882077, 71678999, 215102533, 645438671, 1936578157, 5810258759, 17431824853, 52297571711, 156896909437, 470699116919, 1412114127973
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-6)
Programs
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Magma
[5*3^n/3+0^n/3-2^n: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
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Mathematica
Join[{1},LinearRecurrence[{5,-6},{3,11},30]] (* Harvey P. Dale, Jan 20 2014 *)
Formula
a(n) = 5*3^n/3 + 0^n/3 - 2^n.
G.f.: (1 - 2*x + 2*x^2)/((1-2*x)*(1-3*x)).
E.g.f.: 5*exp(3*x)/3 - exp(2*x) + exp(0)/3.
a(n) = A090888(n-1, 5), for n > 0. - Ross La Haye, Sep 21 2004
a(n) = 5*a(n-1) - 6*a(n-2). - Wesley Ivan Hurt, May 09 2022