cp's OEIS Frontend

A026634 a(n) = Sum_{k=0..floor(n/2)} A026626(n, k).

%I A026634 #9 Jun 21 2024 17:15:05
%S A026634 1,1,4,5,15,22,59,90,230,362,902,1450,3551,5802,14022,23210,55492,
%T A026634 92842,219974,371370,873101,1485482,3468893,5941930,13793183,23767722,
%U A026634 54880915,95070890,218480607,380283562,870164852,1521134250
%N A026634 a(n) = Sum_{k=0..floor(n/2)} A026626(n, k).
%H A026634 G. C. Greubel, <a href="/A026634/b026634.txt">Table of n, a(n) for n = 0..1000</a>
%F A026634 a(n) = floor(A026633(n)/2) if (n mod 2) = 1 and a(n) = floor((2*A026633(n) + (1+(-1)^n)*A026627(floor(n/2)+1))/4) if (n mod 2) = 0. - _G. C. Greubel_, Jun 21 2024
%t A026634 T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, (6*n-1 + (-1)^n)/4, T[n-1,k-1] +T[n-1,k]]];
%t A026634 A026634[n_]:= Sum[T[n,k], {k,0,n}];
%t A026634 Table[A026634[n], {n,0,40}] (* _G. C. Greubel_, Jun 21 2024 *)
%o A026634 (Magma)
%o A026634 b:= func< n | n le 2 select 2*n-1 else ((357*n^3-2696*n^2+6441*n-4822)*Self(n-1) +2*(2*n-7)*(51*n^2-203*n+188)*Self(n-2))/(2*(n-1)*(51*n^2-305*n+442)) >;
%o A026634 A026627:= [b(n+1) : n in [0..60]];
%o A026634 A026633:= [n le 1 select n+1 else (17*2^(n-2) +(-1)^n)/3 -1: n in [0..60]];
%o A026634 function A026634(n)
%o A026634   if (n mod 2) eq 1 then return Floor(A026633[n+1]/2);
%o A026634   else return Floor( (2*A026633[n+1] + (1+(-1)^n)*A026627[Floor(n/2) +1])/4);
%o A026634   end if;
%o A026634 end function;
%o A026634 [A026634(n): n in [0..60]]; // _G. C. Greubel_, Jun 21 2024
%o A026634 (SageMath)
%o A026634 @CachedFunction
%o A026634 def T(n, k): # T = A026626
%o A026634     if (k==0 or k==n): return 1
%o A026634     elif (k==1 or k==n-1): return int(3*n//2)
%o A026634     else: return T(n-1, k-1) + T(n-1, k)
%o A026634 def A026634(n): return sum(T(n,k) for k in range((n//2)+1))
%o A026634 [A026634(n) for n in range(41)] # _G. C. Greubel_, Jun 21 2024
%Y A026634 Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.
%Y A026634 Cf. A026633, A026635, A026636, A026961, A026962, A026963, A026964.
%Y A026634 Cf. A026965.
%K A026634 nonn
%O A026634 0,3
%A A026634 _Clark Kimberling_