A171239 Triangle read by rows extracted from convolution product (1,2,3,...) * A002865: (1,1,2,2,4,4,7,8,...)

1, 1, 2, 2, 2, 3, 2, 4, 3, 4, 4, 4, 6, 4, 5, 4, 8, 6, 8, 5, 6, 7, 8, 12, 8, 10, 6, 7, 8, 14, 12, 16, 10, 12, 7, 8, 8, 14, 12, 16, 10, 12, 7, 8, 12, 16, 21, 16, 20, 12, 14, 8, 9, 14, 24, 24, 28, 20, 24, 14, 10, 9, 10

Offset

1,3

Comments

Row sums = A058682 starting (1, 3, 7, 13, 23, 37, 58, 87,...).

Links

Table of n, a(n) for n=1..63.

Formula

Triangle read by rows, ascending diagonals of an array formed by the product of

(1,2,3,...) and (1,1,2,2,4,4,7,8,12,...).

Example

The triangle = upward sloping diagonals of multiplication table:
.
1,..2,..3,..4,..5,..6,..7,...
1,..2,..3,..4,..5,..6,..7,...
2,..4,..6,..8,.10,.12,.14,...
2,..4,..6,..8,.10,.12,.14,...
... First few rows of the triangle =
.
1;
1, 2;
2, 2, 3;
2, 4, 3, 4;
4, 4, 6, 4, 5;
4, 8, 6, 8, 5, 6;
7, 8, 12, 8, 10, 6, 7;
8, 14, 12, 16, 10, 12, 7, 8;
12, 16, 21, 16, 20, 12, 14, 8, 9;
14, 24, 24, 28, 20, 24, 14, 10, 9, 10;
21, 28, 36, 32, 35, 24, 28, 16, 18, 10, 11;
24, 42, 42, 48, 40, 42, 28, 32, 18, 20, 11, 12;
34, 48, 63, 56, 60, 48, 49, 32, 36, 20, 22, 12, 13;
41, 68, 72, 84, 70, 72, 56, 56, 36, 40, 22, 24, 13, 14;
...

Crossrefs

Cf. A002865, A058682

Sequence in context: A125749 A014085 A248891 * A029210 A321909 A346598

Adjacent sequences: A171236 A171237 A171238 * A171240 A171241 A171242

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 05 2009

Status

approved