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A051473
a(n) = A028321(n)/2.
1
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
0,1
LINKS
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 *)
PROG
(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
(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
KEYWORD
nonn
STATUS
approved