A027050 a(n) = T(n,2n-1), T given by A027023.

1, 3, 5, 11, 25, 59, 145, 367, 949, 2495, 6645, 17883, 48541, 132711, 365073, 1009647, 2805365, 7827167, 21918997, 61584891, 173550677, 490408623, 1389206065, 3944231887, 11221911849, 31989733339, 91354992405, 261322661051

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..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-1), n=1..30); # G. C. Greubel, Nov 05 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[T[n, 2*n-1], {n,30}] (* G. C. Greubel, Nov 05 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-1) for n in (1..30)] # G. C. Greubel, Nov 05 2019

Formula

Conjecture D-finite with recurrence (-n+1)*a(n) +3*(2*n-3)*a(n-1) +(-7*n+10)*a(n-2) +2*(-4*n+19)*a(n-3) +(5*n-23)*a(n-4) +(2*n-5)*a(n-5) +3*(n-4)*a(n-6)=0. - R. J. Mathar, Jun 24 2020

a(n) ~ 3^(n + 5/2) / (4 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 08 2023