A051473 a(n) = A028321(n)/2.

3, 4, 18, 5, 23, 6, 189, 102, 420, 291, 41, 7, 711, 48, 1551, 605, 8, 281, 4433, 2574, 72, 9, 7007, 1456, 81, 10, 39039, 27924, 15834, 7014, 2370, 588, 82654, 66963, 43758, 22848, 9384, 2958, 111, 11, 149617, 110721, 66606, 32232, 12342, 122, 314925

Offset: 0

Author

James Sellers

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A028313, A028314, A028315, A028316, A028317, A028318, A028319.

Cf. A028320, A028321, A028322, A028323, A028324, A028325, A051472.

Programs

Magma

T:= func< n, k | n le 1 select 1 else Binomial(n, k) + 3*Binomial(n-2, k-1) >; // T = A028323
b:=[T(n, k): k in [1+Floor(n/2)..n], n in [0..100]];
[b[n]/2: n in [1..150] | (b[n] mod 2) eq 0]; // G. C. Greubel, Jul 02 2024

Mathematica

b:= Table[If[n<2, 1, Binomial[n,k] +3*Binomial[n-2,k-1]], {n,0,30}, {k, Floor[n/2]+1,n}]//Flatten;
Select[b, EvenQ]/2 (* G. C. Greubel, Jul 02 2024 *)

SageMath

def A028323(n, k): return binomial(n, k) + 3*binomial(n-2, k-1) - 3*int(n==0)
b=flatten([[A028323(n, k) for k in range(1+(n//2),n+1)] for n in range(101)])
[b[n]/2 for n in (1..150) if b[n]%2==0] # G. C. Greubel, Jul 02 2024