A132752 Triangle T(n, k) = 2*A132749(n, k) - 1, read by rows.

1, 3, 1, 3, 3, 1, 3, 5, 5, 1, 3, 7, 11, 7, 1, 3, 9, 19, 19, 9, 1, 3, 11, 29, 39, 29, 11, 1, 3, 13, 41, 69, 69, 41, 13, 1, 3, 15, 55, 111, 139, 111, 55, 15, 1, 3, 17, 71, 167, 251, 251, 167, 71, 17, 1

Offset

0,2

Links

G. C. Greubel, Rows n = 0..100 of the triangle, flattened

Formula

T(n, k) = 2*A132749(n, k) - 1, an infinite lower triangular matrix.

From G. C. Greubel, Feb 16 2021: (Start)

T(n, k) = A109128(n, k) with T(n, 0) = 3.

Sum_{k=0..n} T(n, k) = 2^(n+1) -n +1 -2*[n=0] = A132753(n) - 2*[n=0]. (End)

Example

First few rows of the triangle are:
  1;
  3,  1;
  3,  3,  1;
  3,  5,  5,  1;
  3,  7, 11,  7,  1;
  3,  9, 19, 19,  9,  1;
  3, 11, 29, 39, 29, 11, 1;
  ...

Mathematica

T[n_, k_]:= If[k==n, 1, If[k==0, 3, 2*Binomial[n, k] -1 ]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 16 2021 *)

Prog

(Sage)
def A132752(n, k): return 1 if k==n else 3 if k==0 else 2*binomial(n, k) -1
flatten([[A132752(n, k) for k in [0..n]] for n in [0..12]]) # G. C. Greubel, Feb 16 2021
(Magma)
A132752:= func< n, k | k eq n select 1 else k eq 0 select 3 else 2*Binomial(n, k) -1 >;
[A132752(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 16 2021

Crossrefs

Cf. A109128, A132749, A132753.

Sequence in context: A234308 A050141 A274773 * A131241 A133599 A256399

Adjacent sequences: A132749 A132750 A132751 * A132753 A132754 A132755

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 28 2007

Status

approved