login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A070081 Middle side of integer triangles [A070080(n) <= a(n) <= A070082(n)], sorted by perimeter, sides lexicographically ordered. 73
1, 2, 2, 3, 2, 3, 4, 3, 3, 4, 3, 5, 4, 3, 4, 5, 4, 4, 6, 5, 4, 5, 4, 6, 5, 4, 5, 7, 6, 5, 6, 4, 5, 5, 7, 6, 5, 6, 5, 8, 7, 6, 7, 5, 6, 5, 6, 8, 7, 6, 7, 5, 6, 6, 9, 8, 7, 8, 6, 7, 5, 6, 7, 6, 9, 8, 7, 8, 6, 7, 6, 7, 10, 9, 8, 9, 7, 8, 6, 7, 8, 6, 7, 7, 10, 9, 8, 9, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A070080(n) + a(n) + A070082(n) = A070083(n).

LINKS

G. C. Greubel, Table of n, a(n) for the first 55 rows, flattened

R. Zumkeller, Integer-sided triangles

MATHEMATICA

maxPer = 22; maxSide = Floor[(maxPer-1)/2]; order[{a_, b_, c_}] := (a+b+c)*maxPer^3 + a*maxPer^2 + b*maxPer + c; triangles = Reap[Do[If[ a+b+c <= maxPer && c-b < a < c+b && b-a < c < b+a && c-a < b < c+a, Sow[{a, b, c}]], {a, 1, maxSide}, {b, a, maxSide}, {c, b, maxSide}]][[2, 1]]; Sort[triangles, order[#1] < order[#2] &] [[All, 2]](* Jean-François Alcover, Jun 12 2012 *)

maxPer = m = 22; sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2&]; triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]]&]; triangles[[All, 2]] (* Jean-François Alcover, Jul 9 2017 *)

CROSSREFS

Cf. A046129, A070084, A070085, A070086, A055593, A069595, A069594, A069598.

Sequence in context: A222334 A181948 A238943 * A034883 A071647 A051125

Adjacent sequences:  A070078 A070079 A070080 * A070082 A070083 A070084

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 20 20:52 EST 2019. Contains 320345 sequences. (Running on oeis4.)