

A173304


Triangle generated from the array in A173302 (partition numbers starting new rows at n = 1, 3, 7, 15,...).


4



1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 2, 4, 4, 3, 4, 6, 4, 7, 8, 6, 1, 8, 11, 9, 2, 12, 15, 12, 3, 14, 20, 17, 5, 21, 26, 23, 7, 24, 35, 31, 11, 34, 45, 41, 15, 41, 58, 55, 21, 1, 55, 75, 71, 29, 1, 66, 96, 93, 40, 2, 88, 121, 120, 53, 3, 105, 154, 154, 72, 5, 137, 193, 196, 94, 7
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OFFSET

0,8


COMMENTS

Row sums = A000041, the partition numbers.


LINKS

Table of n, a(n) for n=0..76.


FORMULA

The generating array is in A173302: (A000041 starts again in columns (1, 3, 7, 15,...)
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176,...
...1, 1, 2, 3, 5,..7,.11, 15, 22, 30, 42, 56, .77, 101, 135,...
.........1, 1, 2,..3...5,..7, 11, 15, 22, 30, .42, .56, .77,...
.......................1,..1,..2,..3,..5,..7,..11,..15,..22,...
..........................................................1,...
...
Take finite differences from the bottom, creating a new array in which rows
are A002865(a slight variant), A027336, A027338, A027342,...; i.e. the numbers
of partitions of n that do not contain (1, 2, 4, 8,...) as a part.


EXAMPLE

The finite difference array starts:
1, 1, 1, 1, 2, 2, 4, 4, 7,..8, 12, 14, 21, 24,...; = A002865(a variant)
......1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35,...; = A027336
.........1, 1, 2, 3, 4, 6,..9, 12, 17, 23, 31,...; = A017338
.....................1, 1,..2,..3,..5,..7,.11,...; = A027342
...
...Last, columns of the array become rows of triangle A173304:
1;
1;
1, 1;
2, 2, 1;
2, 3, 2;
4, 4, 3;
4, 6, 4, 1;
7, 8, 6, 1;
8, 11, 9, 2;
12, 15, 12, 3;
14, 20, 17, 5;
21, 26, 23, 7;
24, 35, 31, 11;
34, 45, 41, 15;
41, 58, 55, 21, 1;
55, 75, 71, 29, 1;
66, 96, 93, 40, 2;
88, 121, 120, 53, 3;
105, 154, 154, 72, 5;
137, 193, 196, 94, 7;
...


CROSSREFS

Cf. A000041, A173301, A173302, A173303
Sequence in context: A091423 A221914 A264401 * A029251 A263073 A133091
Adjacent sequences: A173301 A173302 A173303 * A173305 A173306 A173307


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Feb 15 2010


STATUS

approved



