cp's OEIS Frontend

A026632 a(n) = A026626(n, floor(n/2)).

%I A026632 #10 Jun 21 2024 03:53:12
%S A026632 1,1,3,4,8,14,28,49,98,177,354,650,1300,2417,4834,9071,18142,34289,
%T A026632 68578,130360,260720,497928,995856,1909322,3818644,7345470,14690940,
%U A026632 28338826,56677652,109597727,219195454,424761659,849523318
%N A026632 a(n) = A026626(n, floor(n/2)).
%H A026632 G. C. Greubel, <a href="/A026632/b026632.txt">Table of n, a(n) for n = 0..1000</a>
%F A026632 a(n) = (4*(867*n^4 -11934*n^3 +58705*n^2 -123374*n +95280)*a(n-1) +(6069*n^5 -91817*n^4 + 525005*n^3 -1404375*n^2 +1742414*n -803760 )*a(n-2) +2*(867*n^4 - 11934*n^3 +58705*n^2 -123374*n +95280)*a(n-3) + 4*(n-5)*(867*n^4 - 8534*n^3 +28921*n^2 -39246*n +17712)*a(n-4))/(2*(n+1)*(867*n^4 - 12002*n^3 +59725*n^2 -126158*n +95280)), for n >= 6, with a(0) = a(1) = 1, a(2) = 3, a(3) = 4, and a(4) = 8. - _G. C. Greubel_, Jun 20 2024
%t A026632 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 A026632 Table[T[n, Floor[n/2]], {n,0,40}] (* _G. C. Greubel_, Jun 20 2024 *)
%o A026632 (Magma)
%o A026632 [1] cat [n le 4 select Fibonacci(n+2) -(1-(-1)^n)/2 else (4*(867*n^4 - 11934*n^3 +58705*n^2 -123374*n +95280)*Self(n-1) +(6069*n^5 - 91817*n^4 +525005*n^3 -1404375*n^2 +1742414*n -803760)*Self(n-2) +2*(867*n^4 -11934*n^3 +58705*n^2 -123374*n +95280)*Self(n-3) +4*(n-5)*(867*n^4 -8534*n^3 +28921*n^2 -39246*n +17712)*Self(n-4))/(2*(n+1)*(867*n^4 -12002*n^3 +59725*n^2 -126158*n +95280)): n in [1..40]]; // _G. C. Greubel_, Jun 20 2024
%o A026632 (SageMath)
%o A026632 @CachedFunction
%o A026632 def T(n, k): # T = A026626
%o A026632     if (k==0 or k==n): return 1
%o A026632     elif (k==1 or k==n-1): return int(3*n//2)
%o A026632     else: return T(n-1, k-1) + T(n-1, k)
%o A026632 [T(n,int(n//2)) for n in range(41)] # _G. C. Greubel_, Jun 20 2024
%Y A026632 Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026633.
%Y A026632 Cf. A026634, A026635, A026636, A026961, A026962, A026963, A026964.
%Y A026632 Cf. A026965.
%K A026632 nonn
%O A026632 0,3
%A A026632 _Clark Kimberling_