A027031 - OEIS

%I #8 Nov 05 2019 07:23:30

%S 1,3,9,31,105,351,1157,3755,12013,37951,118613,367383,1129345,3449823,

%T 10482869,31713863,95589753,287224199,860773781,2573894583,7681972113,

%U 22890634939,68116073369,202458285647,601159897137

%N a(n) = T(n,2n-7), T given by A027023.

%H G. C. Greubel, <a href="/A027031/b027031.txt">Table of n, a(n) for n = 4..750</a>

%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-7), n=4..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-7], {n,4,30}] (* _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-7) for n in (4..30)] # _G. C. Greubel_, Nov 05 2019

%K nonn

%O 4,2

%A _Clark Kimberling_