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

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..750

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

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 *)

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-1) for n in (1..30)] # G. C. Greubel, Nov 05 2019

Crossrefs

Cf. A027023.

Sequence in context: A285184 A018008 A104545 * A240148 A109249 A196423

Adjacent sequences: A027047 A027048 A027049 * A027051 A027052 A027053

Keyword

nonn

Author

Clark Kimberling

Status

approved