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A354383 Fibonacci sequence beginning 11, 26.

%I A354383 #54 Aug 07 2022 16:00:45
%S A354383 11,26,37,63,100,163,263,426,689,1115,1804,2919,4723,7642,12365,20007,
%T A354383 32372,52379,84751,137130,221881,359011,580892,939903,1520795,2460698,
%U A354383 3981493,6442191,10423684,16865875,27289559,44155434,71444993,115600427,187045420
%N A354383 Fibonacci sequence beginning 11, 26.
%C A354383 The Pisano period of this sequence is equal to the Pisano period of the Fibonacci sequence for all non-multiples of 269.
%D A354383 Aamen Muharram, Investigations of the Gibonacci sequences: Simple Formulae and Gibonacci mod m.
%H A354383 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A354383 a(n) = F(n-4) + L(n+1) + F(n+7).
%F A354383 a(n) = 2*F(n-1) + 3*F(n+4) + 11*F(n).
%F A354383 a(n) = 3*F(n+5) - 2*F(n-3).
%F A354383 a(n) = L(n-3) + L(n+6) - 3*F(n+2), where L(n) is the n-th Lucas number and F(n) is the n-th Fibonacci number.
%F A354383 G.f.: (11+15*x)/(1-x-x^2).
%F A354383 a(n) = 11*F(n-1) + 26*F(n). - _Chai Wah Wu_, Aug 07 2022
%t A354383 LinearRecurrence[{1, 1}, {11, 26}, 35] (* _Amiram Eldar_, Aug 05 2022 *)
%o A354383 (C++) int a[int n]; int * aSequence(){a[0]=11;a[1]=26;for(int i=2;i<n;i++) a[i]=a[i-2]+a[i-1]; return a;}
%o A354383 (Python)
%o A354383 from gmpy2 import fib2
%o A354383 def A354383(n): return int(26*(a:=fib2(n))[0]+11*a[1]) # _Chai Wah Wu_, Aug 07 2022
%Y A354383 Cf. A000032, A000045.
%K A354383 nonn,easy
%O A354383 0,1
%A A354383 _Aamen Muharram_, Aug 04 2022