A131270 Triangle T(n,k) = 2*A046854(n,k) - 1, read by rows.

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

Offset

0,8

Comments

Row sums = A131269: {1, 2, 3, 6, 11, 20, 35, 60, 101, 168, ...}.

Links

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

Formula

T(n,k) = 2*A046854(n,k) - 1.

Reversed triangle of A131268.

Example

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

Mathematica

Table[2*Binomial[Floor[(n+k)/2], k] - 1, {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 09 2019 *)

Prog

(PARI) T(n, k) = 2*binomial((n+k)\2, k)-1; \\ G. C. Greubel, Jul 09 2019
(Magma) [[2*Binomial(Floor((n+k)/2), k) -1: k in [0..n]]:n in [0..12]]; // G. C. Greubel, Jul 09 2019
(Sage) [[2*binomial(floor((n+k)/2), k) -1 for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jul 09 2019

Crossrefs

Cf. A046854, A065941, A000012, A131268, A131269.

Sequence in context: A243200 A016733 A060234 * A109223 A263009 A283983

Adjacent sequences: A131267 A131268 A131269 * A131271 A131272 A131273

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 23 2007

Status

approved