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A028320 Distinct even elements in the 5-Pascal triangle A028313.

%I A028320 #13 Jul 02 2025 16:01:56
%S A028320 6,12,8,38,10,36,46,130,204,378,462,14,82,582,840,96,1422,1680,16,
%T A028320 1210,3102,562,6204,18,144,5148,8866,162,2912,14014,23166,20,1176,
%U A028320 4740,14028,31668,55848,78078,87230,22,222,5916,18768,45696,87516,133926
%N A028320 Distinct even elements in the 5-Pascal triangle A028313.
%H A028320 G. C. Greubel, <a href="/A028320/b028320.txt">Table of n, a(n) for n = 0..1000</a>
%t A028320 DeleteDuplicates[Table[If[n<2, 1, Binomial[n,k] +3*Binomial[n-2,k-1]], {n,0,30}, {k,0,n}]//Flatten]//Select[EvenQ] (* _G. C. Greubel_, Jul 13 2024 *)
%o A028320 (SageMath)
%o A028320 def A028323(n, k): return 1 if n<2 else binomial(n, k) + 3*binomial(n-2, k-1)
%o A028320 b=flatten([[A028323(n, k) for k in range(n+1)] for n in range(31)])
%o A028320 def a(seq): # order preserving
%o A028320     nd = [] # no duplicates
%o A028320     [nd.append(i) for i in seq if not nd.count(i) and i%2==0]
%o A028320     return nd
%o A028320 a(b) # A028320 # _G. C. Greubel_, Jul 13 2024
%Y A028320 Cf. A028313, A028314, A028315, A028316, A028317, A028318, A028319.
%Y A028320 Cf. A028321, A028322, A028323, A028324, A028325, A051472.
%K A028320 nonn
%O A028320 0,1
%A A028320 _Mohammad K. Azarian_
%E A028320 More terms from _James Sellers_, Dec 08 1999