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

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, 355, 15, 1, 2277, 451, 111, 1, 5379, 3487, 1661, 127, 17, 1, 11583, 2223, 689, 1, 20449, 7371, 833, 19, 1, 43615, 34463, 21385, 10283, 3745, 995, 181, 1, 201, 21, 1

Offset: 0

Author

Mohammad K. Azarian

Keywords

• nonn

Comments

Odd elements of A028323. - G. C. Greubel, Jan 06 2024

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A028313, A028323.

Programs

Magma

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
b:=[T(n, k): k in [0..Floor(n/2)], n in [0..100]];
[b[n]: n in [1..150] | (b[n] mod 2) eq 1]; // G. C. Greubel, Jan 06 2024

Mathematica

A028313[n_, k_]:= If[n<2, 1, Binomial[n,k] + 3*Binomial[n-2, k-1]];
f= Table[A028313[n, k], {n,0,100}, {k,1+Floor[n/2],n}]//Flatten;
b[n_]:= DeleteCases[{f[[n+1]]}, _?EvenQ];
Table[b[n], {n,0,150}]//Flatten (* G. C. Greubel, Jan 06 2024 *)

SageMath

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
b=flatten([[T(n, k) for k in range(1+(n//2))] for n in range(101)])
[b[n] for n in (1..150) if b[n]%2==1] # G. C. Greubel, Jan 06 2024

Extensions

More terms from James Sellers