A201913 Irregular triangle of possible factorizations of the trinomial x^n + A*x^m + B, where A and B are rational with A*B nonzero and n > m.

1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 2, 2, 2, 1, 3, 4, 1, 2, 2, 1, 1, 3, 2, 3, 1, 4, 5, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 3, 3, 3, 1, 1, 4, 2, 4, 1, 5, 6

Offset

2,3

Comments

As shown in the example below, for each n, every row sums to n. The rows are a subset of rows in A080576, which lists all partitions of n in graded reflected lexicographic order. Currently, the rows for n=7 are not proved. They are assumed to be {1, 3, 3}, {1, 2, 4}, {3, 4}, {1, 1, 5}, {2, 5}, {1, 6}, {7}.

Links

Table of n, a(n) for n=2..54.

Andrew Bremner and Maciej Ulas, On the reducibility type of trinomials, arxiv 1112.4267

Example

The first rows:
1, 1
2
1, 1, 1
1, 2
3
1, 1, 2
2, 2
1, 3
4
1, 2, 2
1, 1, 3
2, 3
1, 4
5

Crossrefs

Cf. A178868 (note that the number A multiplies a linear term only).

Sequence in context: A194673 A240595 A083671 * A232463 A325032 A270000

Adjacent sequences: A201910 A201911 A201912 * A201914 A201915 A201916

Keyword

nonn,tabf,more

Author

T. D. Noe, Dec 20 2011

Status

approved