A027028 a(n) = T(n,2n-4), T given by A027023.

1, 1, 5, 17, 53, 161, 477, 1393, 4033, 11617, 33365, 95681, 274209, 785793, 2252509, 6460433, 18542169, 53260481, 153115765, 440572993, 1268830877, 3657435745, 10551936125, 30469329025, 88056216233, 254690980449

Offset

2,3

Links

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

Formula

Conjecture D-finite with recurrence -(n+2)*(n-6)*a(n) +3*(n+1)*(2*n-11)*a(n-1) -n*(7*n-31)*a(n-2) -2*(n-3)*(4*n-19)*a(n-3) +(5*n^2-38*n+84)*a(n-4) +(2*n-5)*(n-3)*a(n-5) +3*(n-3)*(n-4)*a(n-6)=0. - R. J. Mathar, Jun 24 2020

a(n) ~ 3^(n + 5/2) / (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-4), 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-4], {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-4) for n in (2..30)] # G. C. Greubel, Nov 04 2019

Crossrefs

Cf. A027023.

Sequence in context: A088210 A135344 A222160 * A176086 A154992 A048473

Adjacent sequences: A027025 A027026 A027027 * A027029 A027030 A027031

Keyword

nonn

Author

Clark Kimberling

Status

approved