A131086 Triangle read by rows: T(n,k) = 2*binomial(n,k) - (-1)^(n-k) (0 <= k <= n).

1, 3, 1, 1, 5, 1, 3, 5, 7, 1, 1, 9, 11, 9, 1, 3, 9, 21, 19, 11, 1, 1, 13, 29, 41, 29, 13, 1, 3, 13, 43, 69, 71, 41, 15, 1, 1, 17, 55, 113, 139, 113, 55, 17, 1, 3, 17, 73, 167, 253, 251, 169, 71, 19, 1, 1, 21, 89, 241, 419, 505, 419, 241, 89, 21, 1, 3, 21, 111, 329

Offset

0,2

Comments

Row sums = A051049 starting (1, 4, 7, 16, 31, 64, ...).

Links

Table of n, a(n) for n=0..69.

Formula

G.f. = G(t,z) = (1 + 3z - tz - 2tz^2)/((1+z)(1-tz)(1-z-tz)). - Emeric Deutsch, Jun 21 2007

Example

First few rows of the triangle are
  1;
  3,  1;
  1,  5,  1;
  3,  5,  7,  1;
  1,  9, 11,  9,  1;
  3,  9, 21, 19, 11,  1;
  1, 13, 29, 41, 29, 13,  1;
  ...

Maple

T := proc (n, k) if k <= n then 2*binomial(n, k)-(-1)^(n-k) else 0 end if end proc: for n from 0 to 11 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jun 21 2007

Crossrefs

Cf. A000012, A051049.

Sequence in context: A261697 A261698 A124738 * A201669 A069002 A245369

Adjacent sequences: A131083 A131084 A131085 * A131087 A131088 A131089

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 14 2007

Extensions

More terms from Emeric Deutsch, Jun 21 2007

Sequence corrected by N. J. A. Sloane, Sep 30 2007

Status

approved