A159573 Triangle read by rows, A055248 * (A005493 * 0^(n-k))

1, 2, 1, 4, 3, 3, 8, 7, 12, 10, 16, 15, 33, 50, 37, 32, 31, 78, 160, 222, 151, 64, 63, 171, 420, 814, 1057, 674, 128, 127, 360, 990, 2368, 4379, 5392, 3263, 256, 255, 741, 2190, 6031, 14043, 24938, 29367, 17007, 512, 511, 1506, 4660, 14134, 38656, 87620

Offset

0,2

Comments

Row sums = A005493: (1, 3, 10, 37, 151, 674, 3263,...); = row sums of Aitken's array. As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=0..51.

Formula

Triangle read by rows, A055248 * (A005493 * 0^(n-k)); equivalent to the product of triangle A055248 and its own eigensequence (diagonalized with the rest zeros, as an infinite lower triangular matrix).

Example

First few rows of the triangle =
1;
2, 1;
4, 3, 3;
8, 7, 12, 10;
16, 15, 33, 50, 37;
32, 31, 78, 160, 222, 151;
64, 63, 171, 420, 814, 1057, 674;
128, 127, 360, 990, 2368, 4379, 5392, 3263;
256, 255, 741, 2190, 6031, 14043, 24938, 29367, 17007;
512, 511, 1506, 4660, 14134, 38656, 87620, 150098, 170070, 94828;
1024, 1023, 3039, 9680, 31376, 96338, 260164, 574288, 952392, 1043108, 562595;
...
Example: row 3 = (8, 7, 12, 10) = termwise products of (8, 7, 4, 1) and
(1, 1, 3, 10), where (8, 7, 12, 10) = row 3 of triangle A055248.

Crossrefs

Cf. A055248, A005493, A011971

Sequence in context: A134599 A117235 A348684 * A102916 A081234 A105239

Adjacent sequences: A159570 A159571 A159572 * A159574 A159575 A159576

Keyword

eigen,nonn,tabl

Author

Gary W. Adamson, Apr 16 2009

Status

approved