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Fibonacci sequence beginning 7, 15.
3

%I #33 Sep 08 2022 08:44:46

%S 7,15,22,37,59,96,155,251,406,657,1063,1720,2783,4503,7286,11789,

%T 19075,30864,49939,80803,130742,211545,342287,553832,896119,1449951,

%U 2346070,3796021,6142091,9938112,16080203,26018315,42098518,68116833,110215351,178332184

%N Fibonacci sequence beginning 7, 15.

%H Harvey P. Dale, <a href="/A022389/b022389.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.: (7+8*x)/(1-x-x^2). - _Philippe Deléham_, Nov 20 2008

%F a(n) = 7*Fibonacci(n+2) + Fibonacci(n) = 7*Fibonacci(n-1) + 15*Fibonacci(n). - _G. C. Greubel_, Mar 02 2018

%F a(n) = Fibonacci(n+6) + Lucas(n-1). - _Greg Dresden_ and Russ Zimmerman, Mar 03 2022

%p with(combinat,fibonacci): seq(7*fibonacci(n+2)+fibonacci(n),n=0..35); # _Muniru A Asiru_, Mar 03 2018

%t LinearRecurrence[{1,1},{7,15},40] (* _Harvey P. Dale_, Aug 27 2013 *)

%t Table[7*Fibonacci[n+2] + Fibonacci[n], {n, 0, 50}] (* _G. C. Greubel_, Mar 02 2018 *)

%o (PARI) for(n=0, 50, print1(7*fibonacci(n+2) + fibonacci(n), ", ")) \\ _G. C. Greubel_, Mar 02 2018

%o (Magma) [7*Fibonacci(n+2) + Fibonacci(n): n in [0..50]]; // _G. C. Greubel_, Mar 02 2018

%o (GAP) List([0..35],n->7*Fibonacci(n+2)+Fibonacci(n)); # _Muniru A Asiru_, Mar 03 2018

%Y Cf. A000032.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_