|
%I #23 Sep 08 2022 08:44:49
%S 1,3,14,46,133,364,972,2567,6746,17690,46345,121368,317784,832011,
%T 2178278,5702854,14930317,39088132,102334116,267914255,701408690,
%U 1836311858,4807526929,12586268976,32951280048,86267571219,225851433662
%N a(0)=1, a(n) = Fibonacci(2n+4) - (2n+3).
%H G. C. Greubel, <a href="/A027953/b027953.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,5,-1).
%F a(n) = T(2n+1, n+1), T given by A027948.
%F G.f.: (1-2*x+7*x^2-5*x^3+x^4)/((1-3*x+x^2)*(1-x)^2). - _Vladeta Jovovic_, Mar 27 2003
%F a(n) = Sum_{j=0..n} binomial(2*n-j+1, j+2), with a(0)=1. - _G. C. Greubel_, Sep 29 2019
%p with(combinat); seq(`if`(n=0,1, fibonacci(2*n+4) -(3 +2*n)), n=0..40); # _G. C. Greubel_, Sep 29 2019
%t Join[{1},Table[Fibonacci[2n+4]-(2n+3),{n,30}]] (* or *) LinearRecurrence[ {5,-8,5,-1},{1,3,14,46,133},30] (* _Harvey P. Dale_, Oct 04 2017 *)
%o (PARI) vector(40, n, my(m=n-1); if(m==0, 1, fibonacci(2*m+4) -(3 +2*m)) ) \\ _G. C. Greubel_, Sep 29 2019
%o (Magma) [1] cat [Fibonacci(2*n+4) -(3 +2*n): n in [1..40]]; // _G. C. Greubel_, Sep 29 2019
%o (Sage) [1]+[fibonacci(2*n+4) -(3 +2*n) for n in (1..40)] # _G. C. Greubel_, Sep 29 2019
%o (GAP) Concatenation([1], List([1..40], n-> Fibonacci(2*n+4) -(3 +2*n) )); # _G. C. Greubel_, Sep 29 2019
%Y Cf. A000045, A027948.
%K nonn
%O 0,2
%A _Clark Kimberling_
%E More terms from _Vladeta Jovovic_, Mar 27 2003
|
