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A173304 Triangle generated from the array in A173302 (partition numbers starting new rows at n = 1, 3, 7, 15, ...). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
Row sums = A000041, the partition numbers.
LINKS
FORMULA
The generating array is in A173302.
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
Sequence in context: A091423 A221914 A264401 * A029251 A263073 A133091
KEYWORD
nonn,tabf,uned
AUTHOR
Gary W. Adamson, Feb 15 2010
STATUS
approved

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Last modified February 24 02:58 EST 2024. Contains 370288 sequences. (Running on oeis4.)