

A330909


Floor of area of triangle whose sides are consecutive Ulam numbers (A002858).


0



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
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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

Table of n, a(n) for n=1..44.
Wikipedia, Ulam number.


FORMULA

Given a triangle with sides a, b and c, the area A = sqrt(s(sa)(sb)(sc)) 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(sa)(sb)(sc)]; AppendTo[lst, Floor@A], {n, 1, 50}]; lst


CROSSREFS

Cf. A002858, A331729.
Sequence in context: A062475 A186265 A225947 * A281969 A124920 A064934
Adjacent sequences: A330906 A330907 A330908 * A330910 A330911 A330912


KEYWORD

nonn


AUTHOR

Frank M Jackson, May 01 2020


STATUS

approved



