The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A334277 Perimeters of almost-equilateral 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 Index entries for linear recurrences with constant coefficients, signature (4,-1). FORMULA a(n) = 3*A003500(n). a(n) = 3 * ((2 + sqrt(3))^n + (2 - sqrt(3))^n). From Alejandro J. Becerra Jr., Jan 29 2021: (Start) G.f.: -6*x*(x - 2)/(x^2 - 4*x + 1). a(n) = 4*a(n-1) - a(n-2). (End) a(n) = 6 * A001075(n). - Joerg Arndt, Jan 29 2021 E.g.f.: 6*(exp(2*x)*cosh(sqrt(3)*x) - 1). - Stefano Spezia, Jan 29 2021 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. A001075. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 12:16 EST 2021. Contains 349462 sequences. (Running on oeis4.)