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

0,4

Comments

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

Links

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A028313, A028323.

Sequence in context: A179530 A098081 A125234 * A245484 A215503 A371835

Adjacent sequences: A028322 A028323 A028324 * A028326 A028327 A028328

Keyword

nonn

Author

Mohammad K. Azarian

Extensions

More terms from James A. Sellers

Status

approved