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%I #15 Mar 08 2023 04:11:11
%S 1,3,5,11,25,59,145,367,949,2495,6645,17883,48541,132711,365073,
%T 1009647,2805365,7827167,21918997,61584891,173550677,490408623,
%U 1389206065,3944231887,11221911849,31989733339,91354992405,261322661051
%N a(n) = T(n,2n-1), T given by A027023.
%H G. C. Greubel, <a href="/A027050/b027050.txt">Table of n, a(n) for n = 1..750</a>
%F 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
%F a(n) ~ 3^(n + 5/2) / (4 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Mar 08 2023
%p T:= proc(n, k) option remember;
%p if k<3 or k=2*n then 1
%p else add(T(n-1, k-j), j=1..3)
%p fi
%p end:
%p seq(T(n,2*n-1), n=1..30); # _G. C. Greubel_, Nov 05 2019
%t 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 *)
%o (Sage)
%o @CachedFunction
%o def T(n, k):
%o if (k<3 or k==2*n): return 1
%o else: return sum(T(n-1, k-j) for j in (1..3))
%o [T(n, 2*n-1) for n in (1..30)] # _G. C. Greubel_, Nov 05 2019
%Y Cf. A027023.
%K nonn
%O 1,2
%A _Clark Kimberling_
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