%I #26 Dec 26 2025 18:54:43

%S 3,15,18,33,51,84,135,219,354,573,927,1500,2427,3927,6354,10281,16635,

%T 26916,43551,70467,114018,184485,298503,482988,781491,1264479,2045970,

%U 3310449,5356419,8666868,14023287,22690155,36713442,59403597,96117039,155520636

%N Fibonacci sequence beginning 3, 15.

%H Harvey P. Dale, <a href="/A022381/b022381.txt">Table of n, a(n) for n = 0..1000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).

%F G.f.: (3+12*x)/(1-x-x^2). - _Philippe Deléham_, Nov 19 2008

%F From _G. C. Greubel_, Dec 25 2025: (Start)

%F a(n) = 3*A022095(n).

%F E.g.f.: 3*(cosh(sqrt(5)*x/2) + (9/sqrt(5))*sinh(sqrt(5)*x/2))*exp(x/2). (End)

%t LinearRecurrence[{1,1},{3,15},40] (* _Harvey P. Dale_, May 27 2012 *)

%o (Magma)

%o [3*GeneralizedFibonacciNumber(1, 5, n): n in [0..50]]; // _G. C. Greubel_, Dec 25 2025

%o (SageMath)

%o A022381= BinaryRecurrenceSequence(1,1,3,15)

%o print([A022381(n) for n in range(51)]) # _G. C. Greubel_, Dec 25 2025

%Y Cf. A000045, A022095.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_