A131129 3*A007318 - 2*A097806, where A007318 = Pascal's triangle and A097806 = the pairwise operator.

1, 1, 1, 3, 4, 1, 3, 9, 7, 1, 3, 12, 18, 10, 1, 3, 15, 30, 30, 13, 1, 3, 18, 45, 60, 45, 16, 1, 3, 21, 63, 105, 105, 63, 19, 1, 3, 24, 84, 168, 210, 168, 84, 22, 1

Offset

0,4

Comments

Row sums = A131128: (1, 2, 8, 20, 44, 92, 188, 380, ...), the binomial transform of (1, 1, 5, 1, 5, 1, 5, ...). Triangle A131108 has row sums (1, 2, 6, 14, 30, 62, ...), the binomial transform of (1, 1, 3, 1, 3, 1, ...). Generalization: Given triangles generated from N*A007318 - (N-1)*A097806, row sums are binomial transforms of (1, 1, (2N-1), 1, (2N-1), 1, ...).

Triangle T(n,k), 0 <= k <= n, read by rows given by [1,2,-3,1,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Dec 18 2007

Links

Table of n, a(n) for n=0..44.

Formula

G.f.: (1-x*y+2*x^2+2*x^2*y)/((-1+x+x*y)*(x*y-1)). - R. J. Mathar, Aug 12 2015

Example

First few rows of the triangle:
  1;
  1,  1;
  3,  4,  1;
  3,  9,  7,  1;
  3, 12, 18, 10,  1;
  3, 15, 30, 30, 13,  1;
  ...

Crossrefs

Cf. A097806, A131128, A095121.

Sequence in context: A169782 A131228 A238558 * A087694 A010262 A378038

Adjacent sequences: A131126 A131127 A131128 * A131130 A131131 A131132

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 16 2007

Status

approved