A027027 - OEIS

%I #16 Sep 22 2025 16:00:28

%S 1,3,9,27,77,215,597,1655,4593,12775,35629,99651,279501,786071,

%T 2216437,6264663,17746897,50380895,143307269,408388819,1165819757,

%U 3333448075,9545909641,27375525727,78612676241,226034151539,650692800633

%N a(n) = T(n, 2n-3), T given by A027023.

%H G. C. Greubel, <a href="/A027027/b027027.txt">Table of n, a(n) for n = 2..750</a>

%F Conjecture: D-finite with recurrence (n+1)*a(n) +(-8*n-1)*a(n-1) +(19*n-14)*a(n-2) +2*(-3*n-1)*a(n-3) +(-21*n+89)*a(n-4) +(8*n-45)*a(n-5) +(n-4)*a(n-6) +6*(n-4)*a(n-7)=0. - _R. J. Mathar_, Jun 24 2020

%F a(n) ~ 3^(n + 7/2) / (4*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Mar 08 2023

%p T:= proc(n, k) option remember;

%p       if k<3 or k=2*n then 1

%p     else add(T(n-1, k-j), j=1..3)

%p       fi

%p     end:

%p seq(T(n, 2*n-3), n=2..30); # _G. C. Greubel_, Nov 04 2019

%t T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]; Table[T[n, 2*n-3], {n, 2, 30}] (* _G. C. Greubel_, Nov 04 2019 *)

%o (SageMath)

%o @CachedFunction

%o def T(n, k):

%o     if (k<3 or k==2*n): return 1

%o     else: return sum(T(n-1, k-j) for j in (1..3))

%o [T(n, 2*n-3) for n in (2..30)] # _G. C. Greubel_, Nov 04 2019

%Y Cf. A027023.

%K nonn

%O 2,2

%A _Clark Kimberling_