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A027027
a(n) = T(n, 2n-3), T given by A027023.
2
1, 3, 9, 27, 77, 215, 597, 1655, 4593, 12775, 35629, 99651, 279501, 786071, 2216437, 6264663, 17746897, 50380895, 143307269, 408388819, 1165819757, 3333448075, 9545909641, 27375525727, 78612676241, 226034151539, 650692800633
OFFSET
2,2
LINKS
FORMULA
Conjecture: D-finite with recurrence (n+1)*a(n) +(-8*n-1)*a(n-1) +(19*n-14)*a(n-2) +2*(-3*n-1)*a(n-3) +(-21*n+89)*a(n-4) +(8*n-45)*a(n-5) +(n-4)*a(n-6) +6*(n-4)*a(n-7)=0. - R. J. Mathar, Jun 24 2020
a(n) ~ 3^(n + 7/2) / (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-3), 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-3], {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-3) for n in (2..30)] # G. C. Greubel, Nov 04 2019
CROSSREFS
Cf. A027023.
Sequence in context: A228734 A048481 A269488 * A361845 A140348 A139561
KEYWORD
nonn
STATUS
approved