cp's OEIS Frontend

A026766 a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026758.

%I A026766 #8 Nov 01 2019 03:54:53
%S A026766 1,1,3,5,13,24,59,115,273,552,1278,2655,6031,12795,28632,61775,136572,
%T A026766 298764,653948,1447225,3141427,7020833,15132512,34106865,73069892,
%U A026766 165903082,353576829,807957495,1714132308,3939206346
%N A026766 a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026758.
%H A026766 G. C. Greubel, <a href="/A026766/b026766.txt">Table of n, a(n) for n = 0..1000</a>
%p A026766 T:= proc(n,k) option remember;
%p A026766    if n<0 then 0;
%p A026766    elif k=0 or k = n then 1;
%p A026766    elif type(n,'odd') and k <= (n-1)/2 then
%p A026766         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026766    else
%p A026766        procname(n-1,k-1)+procname(n-1,k) ;
%p A026766    end if ;
%p A026766 end proc;
%p A026766 seq( add(T(n,k), k=0..floor(n/2)), n=0..30); # _G. C. Greubel_, Oct 31 2019
%t A026766 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[OddQ[n] && k<=(n - 1)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]]; Table[Sum[T[n,k], {k,0,Floor[n/2]}], {n, 0, 30}] (* _G. C. Greubel_, Oct 31 2019 *)
%o A026766 (Sage)
%o A026766 @CachedFunction
%o A026766 def T(n, k):
%o A026766     if (n<0): return 0
%o A026766     elif (k==0 or k==n): return 1
%o A026766     elif (mod(n,2)==1 and k<=(n-1)/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026766     else: return T(n-1,k-1) + T(n-1,k)
%o A026766 [sum(T(n, k) for k in (0..floor(n/2))) for n in (0..30)] # _G. C. Greubel_, Oct 31 2019
%Y A026766 Cf. A026758, A026759, A026760, A026761, A026762, A026763, A026764, A026765, A026767, A026768.
%K A026766 nonn
%O A026766 0,3
%A A026766 _Clark Kimberling_