A094344 Triangle T(n,k), 0<= k <= n, read by rows; given by [0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, ...] DELTA [1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, ...] where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 1, 0, 2, 4, 1, 0, 6, 18, 13, 1, 0, 24, 96, 119, 46, 1, 0, 120, 600, 1059, 777, 199, 1, 0, 720, 4320, 9890, 10760, 5536, 1072, 1, 0, 5040, 35280, 99158, 142990, 111316, 44228, 6985, 1, 0, 40320, 322560, 1073692, 1926312, 2009578, 1217352, 395865, 53218, 1

Offset

0,8

Links

Table of n, a(n) for n=0..54.

Formula

Sum_{k=0..n} T(n,k)*3^(n-k) = A128709(n). - Philippe Deléham, Mar 27 2007

Example

Triangle begins:
  1;
  0,  1;
  0,  1,  1;
  0,  2,  4,   1;
  0,  6, 18,  13,  1;
  0, 24, 96, 119, 46, 1;
  ...

Crossrefs

Row sums: A094664.

Columns: A000007, A000142, A001563.

Diagonals: A000012, A014145.

Sequence in context: A164268 A294390 A152433 * A211183 A137391 A276207

Adjacent sequences: A094341 A094342 A094343 * A094345 A094346 A094347

Keyword

nonn,tabl

Author

Philippe Deléham, Jun 02 2004

Extensions

Row 9 completed by Michel Marcus, Jun 20 2023

Status

approved