%I #16 Jul 02 2025 16:01:56

%S 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 355,15,1,2277,451,111,1,5379,3487,1661,127,17,1,11583,2223,689,1,

%U 20449,7371,833,19,1,43615,34463,21385,10283,3745,995,181,1,201,21,1

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

%C Odd elements of A028323. - _G. C. Greubel_, Jan 06 2024

%H G. C. Greubel, <a href="/A028325/b028325.txt">Table of n, a(n) for n = 0..1000</a>

%t A028313[n_, k_]:= If[n<2, 1, Binomial[n,k] + 3*Binomial[n-2, k-1]];

%t f= Table[A028313[n, k], {n,0,100}, {k,1+Floor[n/2],n}]//Flatten;

%t b[n_]:= DeleteCases[{f[[n+1]]}, _?EvenQ];

%t Table[b[n], {n,0,150}]//Flatten (* _G. C. Greubel_, Jan 06 2024 *)

%o (Magma)

%o 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 b:=[T(n, k): k in [0..Floor(n/2)], n in [0..100]];

%o [b[n]: n in [1..150] | (b[n] mod 2) eq 1]; // _G. C. Greubel_, Jan 06 2024

%o (SageMath)

%o 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 b=flatten([[T(n, k) for k in range(1+(n//2))] for n in range(101)])

%o [b[n] for n in (1..150) if b[n]%2==1] # _G. C. Greubel_, Jan 06 2024

%Y Cf. A028313, A028323.

%K nonn

%O 0,4

%A _Mohammad K. Azarian_

%E More terms from _James Sellers_