A027051 a(n) = T(n,2n-2), T given by A027023.

1, 5, 13, 33, 85, 221, 581, 1545, 4149, 11237, 30657, 84169, 232361, 644573, 1795717, 5021801, 14091829, 39665893, 111965785, 316857945, 898797441, 2555025821, 7277679961, 20767821489, 59365259065, 169967668645, 487356812589

Offset

2,2

Links

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

Formula

Conjecture: D-finite with recurrence n*a(n) +(-7*n+5)*a(n-1) +(13*n-18)*a(n-2) +(n-13)*a(n-3) +(-13*n+64)*a(n-4) +(3*n-25)*a(n-5) +(-n+2)*a(n-6) +3*(n-5)*a(n-7)=0. - R. J. Mathar, Jun 24 2020

a(n) ~ 3^(n + 5/2) / (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-2), n=2..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-2], {n, 2, 30}] (* G. C. Greubel, Nov 05 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-2) for n in (2..30)] # G. C. Greubel, Nov 05 2019

Crossrefs

Cf. A027023.

Sequence in context: A185454 A278764 A183774 * A109786 A283959 A055426

Adjacent sequences: A027048 A027049 A027050 * A027052 A027053 A027054

Keyword

nonn

Author

Clark Kimberling

Status

approved