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A027050
a(n) = T(n,2n-1), T given by A027023.
2
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
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
KEYWORD
nonn
STATUS
approved