A051472 a(n) = A028317(n)/2.

3, 3, 6, 4, 4, 19, 5, 18, 18, 5, 23, 65, 23, 6, 6, 102, 189, 231, 189, 102, 7, 41, 291, 420, 420, 291, 41, 7, 48, 711, 840, 711, 48, 8, 605, 1551, 1551, 605, 8, 281, 3102, 281, 9, 72, 2574, 4433, 4433, 2574, 72, 9, 81, 1456, 7007, 11583, 7007, 1456, 81, 10, 10, 588

Offset: 0

Author

James Sellers

Keywords

• nonn
• tabf

Examples

			Even elements of (1/2)*A028317 as an irregular triangle:
   3,  3;
   6;
   4,  4;
  19;
   5, 18, 18, 5;
  23, 65, 23;
   6,  6;
  ...
		

Links

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

Crossrefs

Cf. A028313, A028317.

Programs

Magma

A028313:= func< n, k | n le 1 select 1 else Binomial(n, k) +3*Binomial(n-2, k-1) >;
a:=[A028313(n, k): k in [0..n], n in [0..100]];
[a[n]/2: n in [1..200] | (a[n] mod 2) eq 0]; // G. C. Greubel, Jan 06 2024

Mathematica

A028313[n_, k_]:= If[n<2, 1, Binomial[n,k] +3*Binomial[n-2,k-1]];
f= Table[A028313[n,k], {n,0,100}, {k,0,n}]//Flatten;
b[n_]:= DeleteCases[{f[[n+1]]}, _?OddQ]/2;
Table[b[n], {n,0,200}]//Flatten (* G. C. Greubel, Jan 06 2024 *)

SageMath

def A028313(n, k): return 1 if n<2 else binomial(n, k) + 3*binomial(n-2, k-1)
a=flatten([[A028313(n, k) for k in range(n+1)] for n in range(101)])
[a[n]/2 for n in (0..200) if a[n]%2==0] # G. C. Greubel, Jan 06 2024