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

Author

Mohammad K. Azarian

Keywords

• nonn
• tabf

Examples

			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;
  ...
		

Links

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

Crossrefs

Cf. A028313, A028316, A028325.

Programs

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

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 *)

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

Extensions

More terms from James Sellers