A027027 a(n) = T(n, 2n-3), T given by A027023.

1, 3, 9, 27, 77, 215, 597, 1655, 4593, 12775, 35629, 99651, 279501, 786071, 2216437, 6264663, 17746897, 50380895, 143307269, 408388819, 1165819757, 3333448075, 9545909641, 27375525727, 78612676241, 226034151539, 650692800633

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..750

Crossrefs

Cf. A027023.

Programs

Maple

T:= proc(n, k) option remember;
      if k<3 or k=2*n then 1
    else add(T(n-1, k-j), j=1..3)
      fi
    end:
seq(T(n, 2*n-3), n=2..30); # G. C. Greubel, Nov 04 2019

Mathematica

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 *)

Sage

@CachedFunction
def T(n, k):
    if (k<3 or k==2*n): return 1
    else: return sum(T(n-1, k-j) for j in (1..3))
[T(n, 2*n-3) for n in (2..30)] # G. C. Greubel, Nov 04 2019

Formula

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

a(n) ~ 3^(n + 7/2) / (4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 08 2023