A152538 Triangle read by rows, A027293 * (A152537 * 0^(n-k))

1, 1, 1, 2, 1, 1, 3, 2, 1, 2, 5, 3, 2, 2, 4, 7, 5, 3, 4, 4, 9, 11, 7, 5, 6, 8, 9, 18, 15, 11, 7, 10, 12, 18, 18, 37, 22, 15, 11, 14, 20, 27, 36, 37, 74, 30, 22, 15, 22, 28, 45, 54, 74, 74, 148, 42, 30, 22, 30, 44, 63, 90, 111, 148, 148, 296

Offset

0,4

Comments

Row sums = 2^n.

Right border = A152537, left border = A000041.

Links

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

Formula

Triangle read by rows, M*Q. M = A027293 as an infinite lower triangular matrix with the partition numbers (A000041) in every column. Q = a matrix with A152537 as the main diagonal and the rest zeros.

Example

First few rows of the triangle =
1;
1, 1;
2, 1, 1;
3, 2, 1, 2;
5, 3, 2, 2, 4;
7, 5, 3, 4, 4, 9;
11, 7, 5, 6, 8, 9, 18;
15, 11, 7, 10, 12, 18, 18, 37;
22, 15, 11, 14, 20, 27, 36, 37, 74;
30, 22, 15, 22, 28, 45, 54, 74, 74, 148;
42, 30, 22, 30, 44, 63, 90, 111, 148, 148, 296;
56, 42, 30, 44, 60, 99, 126, 185, 222, 296, 296, 592;
77, 56, 42, 60, 88, 135, 198, 259, 370, 444, 592, 592, 1183;
...
Row 3 = (3, 2, 1, 2) = termwise products of (3, 2, 1, 1) and (1, 1, 1, 2).

Crossrefs

Cf. A152537, A027293, A000041

Sequence in context: A273102 A273104 A367680 * A345033 A329359 A235682

Adjacent sequences: A152535 A152536 A152537 * A152539 A152540 A152541

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 10 2008

Status

approved