|
|
A330909
|
|
Floor of area of triangle whose sides are consecutive Ulam numbers (A002858).
|
|
1
|
|
|
0, 2, 5, 11, 23, 43, 70, 100, 141, 227, 361, 478, 670, 826, 1044, 1183, 1405, 1668, 1960, 2272, 2545, 2889, 3351, 3819, 4267, 4523, 4955, 5669, 6558, 7474, 8203, 8914, 9633, 10813, 12245, 13611, 13972, 14587, 15473, 16798, 17987, 19298, 20229, 21909, 23166
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
It has been proved that three consecutive Ulam numbers U(n) for n > 1 satisfy the triangle inequality. See Wikipedia link below.
|
|
LINKS
|
|
|
FORMULA
|
Given a triangle with sides a, b and c, the area A = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2.
|
|
EXAMPLE
|
a(2) = 2 because the triangle with sides (2, 3, 4) has area 3*sqrt(15)/4 = 2.9047...
|
|
MATHEMATICA
|
lst1 = ReadList["https://oeis.org/A002858/b002858.txt", {Number, Number}]; lst={}; Do[{a, b, c}={lst1[[n]][[2]], lst1[[n+1]][[2]], lst1[[n+2]][[2]]}; s = (a+b+c)/2; A=Sqrt[s(s-a)(s-b)(s-c)]; AppendTo[lst, Floor@A], {n, 1, 50}]; lst
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|