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Binomial transform of generalized Jacobsthal numbers A084170.
3

%I #18 Sep 08 2022 08:45:11

%S 1,3,11,37,119,373,1151,3517,10679,32293,97391,293197,881639,2649013,

%T 7955231,23882077,71678999,215102533,645438671,1936578157,5810258759,

%U 17431824853,52297571711,156896909437,470699116919,1412114127973

%N Binomial transform of generalized Jacobsthal numbers A084170.

%H Vincenzo Librandi, <a href="/A084171/b084171.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6)

%F a(n) = 5*3^n/3 + 0^n/3 - 2^n.

%F G.f.: (1 - 2*x + 2*x^2)/((1-2*x)*(1-3*x)).

%F E.g.f.: 5*exp(3*x)/3 - exp(2*x) + exp(0)/3.

%F a(n) = A090888(n-1, 5), for n > 0. - _Ross La Haye_, Sep 21 2004

%F a(n) = 5*a(n-1) - 6*a(n-2). - _Wesley Ivan Hurt_, May 09 2022

%t Join[{1},LinearRecurrence[{5,-6},{3,11},30]] (* _Harvey P. Dale_, Jan 20 2014 *)

%o (Magma) [5*3^n/3+0^n/3-2^n: n in [0..35]]; // _Vincenzo Librandi_, Jul 05 2011

%Y Cf. A084170, A090888.

%K easy,nonn

%O 0,2

%A _Paul Barry_, May 18 2003