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A028325 Odd elements to the right of the central elements of the 5-Pascal triangle A028313.

%I A028325 #16 Jul 02 2025 16:01:56
%S A028325 1,1,1,7,1,19,1,27,9,1,65,1,101,11,1,231,147,57,1,69,13,1,273,1,855,
%T A028325 355,15,1,2277,451,111,1,5379,3487,1661,127,17,1,11583,2223,689,1,
%U A028325 20449,7371,833,19,1,43615,34463,21385,10283,3745,995,181,1,201,21,1
%N A028325 Odd elements to the right of the central elements of the 5-Pascal triangle A028313.
%C A028325 Odd elements of A028323. - _G. C. Greubel_, Jan 06 2024
%H A028325 G. C. Greubel, <a href="/A028325/b028325.txt">Table of n, a(n) for n = 0..1000</a>
%t A028325 A028313[n_, k_]:= If[n<2, 1, Binomial[n,k] + 3*Binomial[n-2, k-1]];
%t A028325 f= Table[A028313[n, k], {n,0,100}, {k,1+Floor[n/2],n}]//Flatten;
%t A028325 b[n_]:= DeleteCases[{f[[n+1]]}, _?EvenQ];
%t A028325 Table[b[n], {n,0,150}]//Flatten (* _G. C. Greubel_, Jan 06 2024 *)
%o A028325 (Magma)
%o A028325 T:= func< n,k | Binomial(n+1, k+1+Floor((n+1)/2)) + 3*Binomial(n-1, k+Floor((n+1)/2)) >; // T = A028323, essentially
%o A028325 b:=[T(n, k): k in [0..Floor(n/2)], n in [0..100]];
%o A028325 [b[n]: n in [1..150] | (b[n] mod 2) eq 1]; // _G. C. Greubel_, Jan 06 2024
%o A028325 (SageMath)
%o A028325 def T(n, k): return binomial(n+1, k+1+(n+1)//2) + 3*binomial(n-1, k+((n+1)//2)) - 3*int(n==0) # T = A028323, essentially
%o A028325 b=flatten([[T(n, k) for k in range(1+(n//2))] for n in range(101)])
%o A028325 [b[n] for n in (1..150) if b[n]%2==1] # _G. C. Greubel_, Jan 06 2024
%Y A028325 Cf. A028313, A028323.
%K A028325 nonn
%O A028325 0,4
%A A028325 _Mohammad K. Azarian_
%E A028325 More terms from _James Sellers_