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A028321 Even elements to the right of the central elements of the 5-Pascal triangle A028313.

%I A028321 #13 Jul 02 2025 16:01:56
%S A028321 6,8,36,10,46,12,378,204,840,582,82,14,1422,96,3102,1210,16,562,8866,
%T A028321 5148,144,18,14014,2912,162,20,78078,55848,31668,14028,4740,1176,
%U A028321 165308,133926,87516,45696,18768,5916,222,22,299234,221442,133212
%N A028321 Even elements to the right of the central elements of the 5-Pascal triangle A028313.
%H A028321 G. C. Greubel, <a href="/A028321/b028321.txt">Table of n, a(n) for n = 0..1000</a>
%t A028321 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;
%t A028321 Select[b, EvenQ] (* _G. C. Greubel_, Jul 02 2024 *)
%o A028321 (Magma)
%o A028321 T:= func< n, k | n le 1 select 1 else Binomial(n, k) + 3*Binomial(n-2, k-1) >; // T = A028323
%o A028321 b:=[T(n, k): k in [1+Floor(n/2)..n], n in [0..100]];
%o A028321 [b[n]: n in [1..150] | (b[n] mod 2) eq 0]; // _G. C. Greubel_, Jul 02 2024
%o A028321 (SageMath)
%o A028321 def A028323(n, k): return binomial(n, k) + 3*binomial(n-2, k-1) - 3*int(n==0)
%o A028321 b=flatten([[A028323(n, k) for k in range(1+(n//2),n+1)] for n in range(101)])
%o A028321 [b[n] for n in (1..150) if b[n]%2==0] # _G. C. Greubel_, Jul 02 2024
%Y A028321 Cf. A028313, A028314, A028315, A028316, A028317, A028318, A028319.
%Y A028321 Cf. A028320, A028322, A028323, A028324, A028325, A051472.
%K A028321 nonn,tabf
%O A028321 0,1
%A A028321 _Mohammad K. Azarian_
%E A028321 More terms from _James Sellers_