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A027051
a(n) = T(n,2n-2), T given by A027023.
2
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
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
KEYWORD
nonn
STATUS
approved