A028315 Odd elements in the 5-Pascal triangle A028313.

1, 1, 1, 1, 5, 1, 1, 1, 1, 7, 7, 1, 1, 19, 19, 1, 1, 9, 27, 27, 9, 1, 1, 65, 65, 1, 1, 11, 101, 101, 11, 1, 1, 57, 147, 231, 231, 147, 57, 1, 1, 13, 69, 69, 13, 1, 1, 273, 273, 1, 1, 15, 355, 855, 855, 355, 15, 1, 1, 111, 451, 2277, 2277, 451, 111, 1, 1, 17, 127, 1661, 3487, 5379, 5379, 3487, 1661, 127, 17, 1

Offset

0,5

Links

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

Example

Odd elements of A028313 as an irregular triangle:
  1;
  1,   1;
  1,   5,   1;
  1,   1;
  1,   7,   7,   1;
  1,  19,  19,   1;
  1,   9,  27,  27,   9,   1;
  1,  65,  65,   1;
  1,  11, 101, 101,  11,   1;
  1,  57, 147, 231, 231, 147, 57, 1;
  1,  13,  69,  69,  13,   1;
  1, 273, 273,   1;
  1,  15, 355, 855, 855, 355, 15, 1;
  ...

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, 0, n}]//Flatten;
a[n_]:= DeleteCases[{f[[n+1]]}, _?EvenQ];
Table[a[n], {n, 0, 150}]//Flatten (* G. C. Greubel, Jan 06 2024 *)

Prog

(Magma)
A028313:= func< n, k | n le 1 select 1 else Binomial(n, k) +3*Binomial(n-2, k-1) >;
a:=[A028313(n, k): k in [0..n], n in [0..100]];
[a[n]: n in [1..150] | (a[n] mod 2) eq 1]; // G. C. Greubel, Jan 06 2024
(SageMath)
def A028313(n, k): return 1 if n<2 else binomial(n, k) + 3*binomial(n-2, k-1)
a=flatten([[A028313(n, k) for k in range(n+1)] for n in range(101)])
[a[n] for n in (0..150) if a[n]%2==1] # G. C. Greubel, Jan 06 2024

Crossrefs

Cf. A028313, A028316, A028325.

Sequence in context: A071020 A046601 A101025 * A074062 A094635 A358347

Adjacent sequences: A028312 A028313 A028314 * A028316 A028317 A028318

Keyword

nonn,tabf

Author

Mohammad K. Azarian

Extensions

More terms from James A. Sellers

Status

approved