login
a(n) = T(2n+1, n+3), T given by A027948.
1

%I #13 Sep 08 2022 08:44:49

%S 1,7,92,591,2683,9955,32551,98086,280271,773906,2091266,5576298,

%T 14750858,38839257,101995694,267462041,700813797,1835540197,

%U 4806538617,12585017712,32949712457,86265626164,225849041524,591283811748,1548005222980,4052735290427,10610204784368

%N a(n) = T(2n+1, n+3), T given by A027948.

%H G. C. Greubel, <a href="/A027955/b027955.txt">Table of n, a(n) for n = 2..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (9,-34,71,-90,71,-34,9,-1).

%F G.f.: x^2*(1 -2*x +63*x^2 -70*x^3 +85*x^4 -71*x^5 +34*x^6 -9*x^7 +x^8)/( (1-x)^6*(1-3*x+x^2)). - _Colin Barker_, Nov 25 2014

%F From _G. C. Greubel_, Sep 30 2019: (Start)

%F a(n) = Sum_{j=0..n-2} binomial(2*n-j+1, j+6) for n >= 3.

%F a(n) = Fibonacci(2*n+8) - (630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30 for n >= 3. (End)

%p with(combinat); seq(`if`(n=2,1, fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30), n=2..40); # _G. C. Greubel_, Sep 30 2019

%t Table[If[n==2, 1, Fibonacci[2*n+8] - (630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30], {n,2,40}] (* _G. C. Greubel_, Sep 30 2019 *)

%o (PARI) vector(40, n, my(m=n+1); if(m==2, 1, fibonacci(2*m+8) -(630 +607*m +295*m^2 +90*m^3 +20*m^4 +8*m^5)/30) ) \\ _G. C. Greubel_, Sep 30 2019

%o (Magma) [1] cat [Fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30: n in [3..40]]; // _G. C. Greubel_, Sep 30 2019

%o (Sage) [1]+[fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30 for n in (3..40)] # _G. C. Greubel_, Sep 30 2019

%o (GAP) Concatenation([1], List([3..40], n-> Fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30) ); # _G. C. Greubel_, Sep 30 2019

%Y Cf. A000045, A027948.

%K nonn

%O 2,2

%A _Clark Kimberling_

%E Name corrected and terms a(22) onward by _G. C. Greubel_, Sep 30 2019