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A028317 Even elements in the 5-Pascal triangle A028313.

%I A028317 #17 Jul 02 2025 16:01:56
%S A028317 6,6,12,8,8,38,10,36,36,10,46,130,46,12,12,204,378,462,378,204,14,82,
%T A028317 582,840,840,582,82,14,96,1422,1680,1422,96,16,1210,3102,3102,1210,16,
%U A028317 562,6204,562,18,144,5148,8866,8866,5148,144,18,162,2912,14014,23166
%N A028317 Even elements in the 5-Pascal triangle A028313.
%H A028317 G. C. Greubel, <a href="/A028317/b028317.txt">Table of n, a(n) for n = 0..1000</a>
%F A028317 a(n) = 2*A051472(n). - _G. C. Greubel_, Jan 06 2024
%e A028317 Even elements of A028313 as an irregular triangle:
%e A028317    6,   6;
%e A028317   12;
%e A028317    8,   8;
%e A028317   38;
%e A028317   10,  36, 36, 10;
%e A028317   46, 130, 46;
%e A028317   12,  12;
%e A028317   ...
%t A028317 A028313[n_, k_]:= If[n<2, 1, Binomial[n,k] +3*Binomial[n-2,k-1]];
%t A028317 f= Table[A028313[n,k], {n,0,100}, {k,0,n}]//Flatten;
%t A028317 b[n_]:= DeleteCases[{f[[n+1]]}, _?OddQ];
%t A028317 Table[b[n], {n,0,200}]//Flatten (* _G. C. Greubel_, Jan 06 2024 *)
%o A028317 (Magma)
%o A028317 A028313:= func< n, k | n le 1 select 1 else Binomial(n, k) +3*Binomial(n-2, k-1) >;
%o A028317 a:=[A028313(n, k): k in [0..n], n in [0..100]];
%o A028317 [a[n]: n in [1..200] | (a[n] mod 2) eq 0]; // _G. C. Greubel_, Jan 06 2024
%o A028317 (SageMath)
%o A028317 def A028313(n, k): return 1 if n<2 else binomial(n, k) + 3*binomial(n-2, k-1)
%o A028317 a=flatten([[A028313(n, k) for k in range(n+1)] for n in range(101)])
%o A028317 [a[n] for n in (0..200) if a[n]%2==0] # _G. C. Greubel_, Jan 06 2024
%Y A028317 Cf. A028313, A051472.
%K A028317 nonn,tabf
%O A028317 0,1
%A A028317 _Mohammad K. Azarian_
%E A028317 More terms from _James Sellers_