A131779 Triangle read by rows: T(n,k) = 2*A065941(n-1,k-1) - (-1)^(n+k).

1, 3, 1, 1, 3, 1, 3, 1, 5, 1, 1, 3, 5, 5, 1, 3, 1, 9, 5, 7, 1, 1, 3, 9, 9, 11, 7, 1, 3, 1, 13, 9, 21, 11, 9, 1, 1, 3, 13, 13, 29, 21, 19, 9, 1, 3, 1, 17, 13, 43, 29, 41, 19, 11, 1, 1, 3, 17, 17, 55, 43, 69, 41, 29, 11, 1, 3, 1, 21, 17, 73, 55, 113, 69, 71, 29, 13, 1

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Formula

T(n,k) = 2*binomial(n-1-floor(k/2), floor((k-1)/2)) - (-1)^(n+k). - Andrew Howroyd, Sep 08 2018

Example

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

Prog

(PARI) T(n, k) = {if(k<=n, 2*binomial(n-1-k\2, (k-1)\2) - (-1)^(n+k), 0)} \\ Andrew Howroyd, Sep 08 2018

Crossrefs

Row sums are A131780.

Cf. A065941.

Sequence in context: A193179 A133705 A046111 * A131775 A218825 A035691

Adjacent sequences: A131776 A131777 A131778 * A131780 A131781 A131782

Keyword

nonn,tabl

Author

Gary W. Adamson, Jul 14 2007

Extensions

a(28)-a(29) corrected and terms a(56) and beyond from Andrew Howroyd, Sep 08 2018

Status

approved