Root regions
Nodes grouped by the interval that contains every root of every row (proved, for all n). A node can have
several proved regions; the sharpest is the smallest interval.
| All roots in | Nodes |
|---|
(-inf, 0] |
2294 |
(-inf, +inf) |
332 |
(-inf, 0) |
258 |
(-inf, -1] |
188 |
[-1, 0] |
147 |
[−3−2√2, −3+2√2]
(rational outer bound [-1564556493/268435456, -46056243/268435456]) |
13 |
[-1, 0) |
13 |
(-inf, 1] |
10 |
(-1, 0) |
6 |
(-5, -1) |
6 |
(-2, 0) |
6 |
[0, +inf) |
6 |
(-4, 0) |
6 |
(-1, 1) |
3 |
(0, 1) |
3 |
(-1, 0] |
3 |
[-4, 0] |
3 |
(-3, 1] |
3 |
(-1, 3] |
3 |
(3, 7] |
3 |
(-4, 0] |
3 |
(-2, -1) |
2 |
[9/2, +inf) |
2 |
(11, 15] |
2 |
(-2, 2) |
2 |
(2, 6] |
2 |
(1, 5] |
2 |
(4, 8] |
2 |
(0, 4] |
2 |
(-2, 2] |
2 |
(5, 9] |
2 |
(-2, 6] |
1 |
[5/2, +inf) |
1 |
(-6, 2] |
1 |
(-inf, 5/2] |
1 |
(131/9, 15] |
1 |
(32/9, 4] |
1 |
(7, 15] |
1 |
[-36, 0) |
1 |
[13/2, +inf) |
1 |
(-4/3, 0] |
1 |
(1, 9] |
1 |
(23/3, 9] |
1 |
(5/9, 1] |
1 |
[-1, +inf) |
1 |
[-4/3, 0] |
1 |
(-3, 1) |
1 |
(-7, -3) |
1 |
(0, 1] |
1 |
(14/9, 2] |
1 |
(4, 6] |
1 |
(77/9, 9] |
1 |
[17/2, +inf) |
1 |
(10, 14] |
1 |
(26/3, 10] |
1 |
(59/9, 7] |
1 |
[-5, -1] |
1 |
(-3, 2) |
1 |
(-8, 0) |
1 |
(0, 4) |
1 |
(2, 10] |
1 |
(41/3, 15] |
1 |
(8, 12] |
1 |
(-1, 3) |
1 |
[2, +inf) |
1 |
(-5, 3] |
1 |
(-inf, 1/2] |
1 |
(3, 7) |
1 |
(6, 8] |
1 |
(-9, -1) |
1 |
(0, 8] |
1 |
(5, 7] |
1 |
(86/9, 10] |
1 |
(-1, 7] |
1 |
(-2, 3) |
1 |
[5, +inf) |
1 |
(-6, 0) |
1 |
(-inf, 3/2] |
1 |
(13, 15] |
1 |
(32/3, 12] |
1 |
(7, 11] |
1 |
[-3/2, +inf) |
1 |
[11/2, +inf) |
1 |
(-4, 4] |
1 |
(-inf, -2] |
1 |
(20/3, 8] |
1 |
(5/3, 3] |
1 |
[-1, -2/3) |
1 |
(-1/3, 1] |
1 |
(-3, -1) |
1 |
[7/2, +inf) |
1 |
(-7, -1) |
1 |
(14/3, 6] |
1 |
(4, 12] |
1 |
(7, 9] |
1 |
[15/2, +inf) |
1 |
(-4/9, 0] |
1 |
(10, 12] |
1 |
(23/9, 3] |
1 |
(50/9, 6] |
1 |
(-2, -1] |
1 |
[-4/9, 0] |
1 |
(-7, 1] |
1 |
(0, 2] |
1 |
(17/3, 7] |
1 |
(8, 10] |
1 |
(-1, 1] |
1 |
[19/2, +inf) |
1 |
(-5, -1] |
1 |
(104/9, 12] |
1 |
(3, 5] |
1 |
(6, 10] |
1 |
[-1/2, +inf) |
1 |
(-2, 0] |
1 |
[-8, 0] |
1 |
(-3, 5] |
1 |
(-8, 0] |
1 |
(2, 4] |
1 |
(41/9, 5] |
1 |
(8/3, 4] |
1 |
[3/2, +inf) |
1 |
(-6, -2) |
1 |
(-inf, 1/4] |
1 |
(11/3, 5] |
1 |
(68/9, 8] |
1 |
[-2, 0] |
1 |
[1, +inf) |
1 |
(1, 3] |
1 |
(2/3, 2] |
1 |
[-1, -1/2) |
1 |
(-1/2, 0] |
1 |
Nodes with all roots in (-2, -1) (2)
-
A063007 → x ↦ x+1
1 · 3, 2 · 13, 18, 6 · 63, 132, 90, 20 …
row sums 1, 5, 37, 305, 2641, 23525, 213445, …
(−2, −1)
nonnegative
-
A033282 → x ↦ x+1
1 · 3, 2 · 11, 15, 5 · 45, 93, 63, 14 …
row sums 1, 5, 31, 215, 1597, 12425, 99955, …
(−2, −1)
nonnegative