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

2,2

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A027023.

Sequence in context: A228734 A048481 A269488 * A361845 A140348 A139561

Adjacent sequences: A027024 A027025 A027026 * A027028 A027029 A027030

Keyword

nonn

Author

Clark Kimberling

Status

approved