A163946 Triangle read by rows, A033184 * A091768 (diagonalized as an infinite lower triangular matrix).

1, 1, 1, 2, 2, 2, 5, 5, 6, 6, 14, 14, 18, 24, 22, 42, 42, 56, 84, 110, 92, 132, 132, 180, 288, 440, 552, 426, 429, 429, 594, 990, 1650, 2484, 2982, 2150, 1430, 1430, 2002, 3432, 6050, 10120, 14910, 17200, 11708, 4862, 4862, 6864, 12012, 22022, 39468, 65604, 94600, 105372, 68282

Offset

0,4

Comments

As an eigentriangle, equals A033184 * the diagonalized version of its eigensequence. (the eigensequence of triangle A033184 = A091768).

Right border = A091768, left border = Catalan sequence A000108.

Sum of n-th row terms = rightmost term of next row.

Links

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

Formula

Triangle read by rows, A033184 * A091768 (diagonalized such that the right border = (1, 1, 2, 6, 22, 92, 426, 2150,...) i.e. A091768 prefaced with a 1; with the rest zeros).

Example

First few rows of the triangle =
  1;
  1, 1;
  2, 2, 2;
  5, 5, 6, 6;
  14, 14, 18, 24, 22;
  42, 42, 56, 84, 110, 92;
  132, 132, 180, 288, 440, 552, 426;
  429, 429, 594, 990, 1650, 2484, 2982, 2150;
  1430, 1430, 2002, 3432, 6050, 10120, 14910, 17200, 11708;
  4862, 4862, 6864, 12012, 22022, 39468, 65604, 94600, 105372, 68282;
  ...
Row 3 = (5, 5, 6, 6) = (5, 5, 3, 1) * (1, 1, 2, 6); where (5, 5, 3, 1) = row 3 of triangle A033184 and (1, 1, 2, 6) = the first 3 terms of A091768 prefaced with a 1.

Crossrefs

Cf. A033184, A091768, A000108, A071721.

Sequence in context: A332966 A035643 A324925 * A240500 A344264 A308512

Adjacent sequences: A163943 A163944 A163945 * A163947 A163948 A163949

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 06 2009

Status

approved