Pierre Abbat has authored 4 sequences.
A361388
Number of orders of distances to vertices of n-dimensional cube.
Original entry on oeis.org
1, 2, 8, 96, 5376, 1981440, 5722536960, 138430238607360
Offset: 0
For n=3, a 3-dimensional cube has 8 corners, numbered 0 to 7. A point can be closest to any of the 8 corners. A point closest to 0 can have distances to corners 1, 2, and 4 in any of 6 orders. A point whose distances to corners 0, 1, 2, and 4 are in increasing order can be closer to 3 than to 4, or closer to 4 than to 3. So the total number of orders is 8*6*2=96.
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A361388(n) = A009997(n)*n!<M. F. Hasler, Mar 10 2023
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def a(n):
x = polygens(QQ,n,'x')
dist2 = [sum((xi - ti)^2 for xi,ti in zip(x,t)) for t in Tuples(range(2),n)] # squared distances
diffs = {p[0]-p[1] for p in Combinations(dist2,2)} # set of pairwise differences of squared distances
H = HyperplaneArrangements(QQ, tuple(map(str,x)))
A = H([[[d.coefficient({xi:1}) for xi in x], d.constant_coefficient()] for d in diffs])
return A.n_regions()
print( [a(n) for n in (1..4)] ) # Max Alekseyev, Mar 10 2023
(C++) // See Cubeorders link.
A336433
Number of sequences of n numbers from 1 to n that do not have a subsequence that adds up to n.
Original entry on oeis.org
0, 0, 0, 1, 5, 68, 403, 7257, 61686, 1174434, 13810620, 335547727, 3783688286, 124486381056, 1935430229612, 55798127869680, 1058567311736669, 39819079382937334, 717447490866241055, 32064848897165970340, 666062878027691348450, 28916070816360797805534
Offset: 0
For n=3, the only solution is 2,2,2.
For n=4, the 5 solutions are 3,3,3,3 and the four permutations of 3,3,3,2.
A322289
Primes sorted by quadratic irrational continued fraction terms.
Original entry on oeis.org
5, 3, 2, 17, 13, 7, 37, 41, 29, 11, 73, 61, 53, 19, 23, 109, 89, 101, 97, 113, 31, 149, 157, 137, 43, 47, 193, 197, 181, 173, 59, 277, 241, 281, 269, 257, 233, 229, 67, 71, 79, 313, 337, 349, 353, 317, 293, 83, 409, 421, 433, 389, 401, 373, 397, 103, 107
Offset: 1
17 == 1 (mod 4), so compute (sqrt(17)+1)/2 = 2.561552812808830.... Its continued fraction expansion is [2;(1,1,3)]. The largest term is 3.
13 == 1 (mod 4), so compute (sqrt(13)+1)/2 = 2.30277563773199.... Its continued fraction expansion is [2;(3)]. The largest term is again 3, but the average term is larger than the average term in (sqrt(17)+1)/2, so 13 goes after 17.
7 == 3 (mod 4), so compute sqrt(7) = 2.645751311064590.... Its continued fraction expansion is [2;(1,1,1,4)]. The largest term is 4, so 7 goes after 13.
A081880
Triangle read by rows: n-th row gives trajectory of 2n under the map x->(x^2-4)/6, stopping when the next term would be negative or nonintegral.
Original entry on oeis.org
0, 2, 0, 4, 2, 0, 6, 8, 10, 16, 42, 10, 16, 42, 12, 14, 32, 170, 4816, 3865642, 2490531345360, 16, 42, 18, 20, 66, 22, 80, 1066, 189392, 5978221610, 5956522269711832016, 5913359591595499145281505571167104042, 5827970276585748074286667660065476529979312208145367609757859954142122960, 24, 26
Offset: 0
8 -> (64-4)/6 = 10 -> (100-4)/6 = 16 -> (256-4)/6 = 42 -> (42^2-4)/6 nonintegral, so stop; thus row 4 is (8, 10, 16, 42).
Triangle begins:
0,
2, 0,
4, 2, 0,
6,
8,
10, 16, 42, 10, 16, 42,
12,
14, 32, 170, 4816, 3865642, 2490531345360,
16, 42,
18,
20, 66,
22, 80, 1066, 189392, 5978221610, 5956522269711832016, 5913359591595499145281505571167104042, 5827970276585748074286667660065476529979312208145367609757859954142122960,
24,
...
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