A133087 A133080 * A007318.

1, 2, 1, 1, 2, 1, 2, 5, 4, 1, 1, 4, 6, 4, 1, 2, 9, 16, 14, 6, 1, 1, 6, 15, 20, 15, 6, 1, 2, 13, 36, 55, 50, 27, 8, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 2, 17, 64, 140, 196, 182, 112, 44, 10, 1

Offset

0,2

Comments

Row sums = A084221: (1, 3, 4, 12, 16, 48, 64, 192, ...).

Subtriangle of (0, 2, -3/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 03 2012

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

A133080 * A007318 as infinite lower triangular matrices.

G.f.: (1+2*x+y*x)/(1-(1+y)^2*x^2). - Philippe Deléham, Mar 03 2012

T(n,k) = T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-1), T(0,0) = 1, T(1,0) = 2, T(1,1) = 1. - Philippe Deléham, Mar 03 2012

Sum_{k=0..n} T(n,k)*x^k = A059841(n), A019590(n+1), A000034(n), A084221(n), A133125(n) for x = -2, -1, 0, 1, 2 respectively. - Philippe Deléham, Mar 03 2012

Example

First few rows of the triangle:
  1;
  2,  1;
  1,  2,  1;
  2,  5,  4,  1;
  1,  4,  6,  4,  1;
  2,  9, 16, 14,  6,  1;
  1,  6, 15, 20, 15,  6,  1;
  2, 13, 36, 55, 50, 27,  8,  1;
  1,  8, 28, 56, 70, 56, 28,  8,  1;
  ...
Triangle (0, 2, -3/2, -1/2, 0, 0, 0, ...) DELTA (1, 0, -1, 0, 0, 0, ...) begins:
  1;
  0,  1;
  0,  2,  1;
  0,  1,  2,  1;
  0,  2,  5,  4,  1;
  0,  1,  4,  6,  4,  1;
  0,  2,  9, 16, 14,  6,  1;
  0,  1,  6, 15, 20, 15,  6,  1;
  0,  2, 13, 36, 55, 50, 27,  8,  1;
  0,  1,  8, 28, 56, 70, 56, 28,  8,  1;
  ...

Mathematica

CoefficientList[CoefficientList[Series[(1 + 2*x + y*x)/(1 - (1 + y)^2*x^2), {x, 0, 10}, {y, 0, 10}], x], y] // Flatten (* G. C. Greubel, Oct 21 2017 *)

Crossrefs

Cf. A133080, A084221.

Columns: A000007, A114752, A133092.

Sequence in context: A193749 A049824 A376580 * A153919 A185286 A153905

Adjacent sequences: A133084 A133085 A133086 * A133088 A133089 A133090

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 08 2007

Status

approved