

A334277


Perimeters of almostequilateral Heronian triangles.


5



12, 42, 156, 582, 2172, 8106, 30252, 112902, 421356, 1572522, 5868732, 21902406, 81740892, 305061162, 1138503756, 4248953862, 15857311692, 59180292906, 220863859932, 824275146822, 3076236727356, 11480671762602, 42846450323052, 159905129529606, 596774067795372, 2227191141651882
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Heronian Triangle
Wikipedia, Heronian triangle
Wikipedia, Integer Triangle


FORMULA

a(n) = 3 * ((2 + sqrt(3))^n + (2  sqrt(3))^n).


EXAMPLE

a(1) = 12; there is one Heronian triangle with perimeter 12 whose side lengths are consecutive integers, [3,4,5].
a(2) = 42; there is one Heronian triangle with perimeter 42 whose side lengths are consecutive integers, [13,14,15].


MATHEMATICA

Table[Expand[3 ((2 + Sqrt[3])^n + (2  Sqrt[3])^n)], {n, 40}]


CROSSREFS

Cf. a(n) = 3*A003500(n).
Cf. A011945 (areas), this sequence (perimeters).
Cf. A003500 (middle side lengths), A016064 (smallest side lengths), A335025 (largest side lengths).
Sequence in context: A193068 A007586 A228391 * A122973 A074356 A172294
Adjacent sequences: A334274 A334275 A334276 * A334278 A334279 A334280


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, May 20 2020


STATUS

approved



