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A027028
a(n) = T(n,2n-4), T given by A027023.
2
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
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
KEYWORD
nonn
STATUS
approved