A153342 Binomial transform of triangle A046854 (shifted).

1, 2, 0, 4, 1, 0, 8, 4, 1, 0, 16, 12, 5, 1, 0, 32, 32, 18, 6, 1, 0, 64, 80, 56, 25, 7, 1, 0, 128, 192, 160, 88, 33, 8, 1, 0, 256, 448, 432, 280, 129, 42, 9, 1, 0, 512, 1024, 1120, 832, 450, 180, 52, 10, 1, 0, 1024, 2304, 2816, 2352, 1452, 681, 242, 63, 11, 1, 0

Offset

0,2

Comments

Row sums = odd indexed Fibonacci numbers.

Mirror image of triangle in A121462. - Philippe Deléham, Dec 31 2008

Triangle T(n,k), 0 <= k <= n, read by rows given by [2,0,0,0,0,0,0,0,0,0,0,0,...] DELTA [0,1/2,1/2,0,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 01 2009

Links

Table of n, a(n) for n=0..65.

Formula

Triangle read by rows, A007318 * A046854 (shifted down 1 row, inserting a "1" at (0,0).

G.f.: (1-y*x)/(1-2*x-y*x+y*x^2). - Philippe Deléham, Mar 27 2012

T(n,k) = 2*T(n-1,l) + T(n-1,k-1) - T(n-2,k-1), T(0,0) = 1, T(1,0) = 2, T(1,1) = 0 and T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 27 2012

Example

First few rows of the triangle =
    1;
    2,    0;
    4,    1,    0;
    8,    4,    1,   0;
   16,   12,    5,   1,   0;
   32,   32,   18,   6,   1,   0;
   64,   80,   56,  25,   7,   1,  0;
  128,  192,  160,  88,  33,   8,  1,  0;
  256,  448,  432, 280, 129,  42,  9,  1, 0;
  512, 1024, 1120, 832, 450, 180, 52, 10, 1, 0;
  ...

Crossrefs

Cf. A046854, A001519.

Sequence in context: A291940 A153345 A140648 * A144258 A056859 A272098

Adjacent sequences: A153339 A153340 A153341 * A153343 A153344 A153345

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 24 2008

Extensions

Second term corrected by Philippe Deléham, Jan 01 2009

Status

approved