Cfrgtkky

I would need a list, possibly an array (for later use in a foreach loop / TikZ graphic), which contains the following values ​​(a_n) in order (n = 1,2,3, ...):

45,135,225,270,315,
45,45,90,135,135,225,225,270,270,315,315,
45,45,45,90,90,135,135,135,225,225,225,315,315,315,
45,45,45,45,90,90,90,135,135,135,135,225,225,225,225,270,270,270,270,315,315,315,315 .........

The system is the following:
1x45, 0x90, 1x other angles
2x45, 1x90, 2x other angles
3x45, 2x90, 3x other angles
4x45, 3x90, 4x other angles
....

Note: I'm not looking for the formula function or anything like that, just looking for a list for TikZ-use.

documentclass[margin=5pt, varwidth]{standalone}

usepackage{tikz}

begin{document}



pgfmathsetmacro{k}{2}



pgfmathsetmacro{Start}{k}

pgfmathsetmacro{End}{k+5}

foreach[evaluate={N=int(n+1)}] n in {Start,...,End}{

pgfmathsetmacro{A}{int(floor(N/2)-floor(N/3))}

n: A~

}



end{document}

documentclass[margin=5pt, varwidth]{standalone}

usepackage{pgffor}

begin{document}

newcommand{AddOtherAngles}[1]{foreach X in {225,270,315}

{foreach Y in {1,...,#1}

{xdefmyList{myList,X}}}}



foreach A [evaluate=A as B using {int(A-1)}] in {1,...,4}

{foreach a in {1,...,A}

 {ifnuma=1

   xdefmyList{45}

  else

   xdefmyList{myList,45}

  fi}

ifnumB>0

foreach b in {1,...,B}

 {xdefmyList{myList,90}}

fi

AddOtherAngles{A}

myListpar

}

end{document}

Everything in one list.

documentclass[margin=5pt, varwidth]{standalone}

usepackage{tikz}

begin{document}



foreach A [evaluate=A as B using {int(A-1)}] in {1,...,4}

{foreach a in {1,...,A}

 {ifnuma=1

    ifnumA=1

     xdefmyList{45}

    else

     xdefmyList{myList,45}

    fi

  else

   xdefmyList{myList,45}

  fi}

ifnumB>0

foreach b in {1,...,B}

 {xdefmyList{myList,90}}

fi

foreach X in {225,270,315}

{foreach Y in {1,...,A}

{xdefmyList{myList,X}}}

}

typeout{myList}



tikz{foreach w in myList { draw (0,0)--(w:1); } }



end{document}

With expl3:

documentclass{article}

usepackage{xparse}



ExplSyntaxOn



NewDocumentCommand{generatelist}{mm}

 {% #1 = control sequence, #2 = number of repetitions

  genlist_main:nn { #1 } { #2 }

 }



cs_new_protected:Nn genlist_main:nn

 {

  tl_set:Nx l_tmpa_tl

   {

    45

    prg_replicate:nn { #2-1 } { ,45  }

    prg_replicate:nn { #2-1 } { ,90  }

    prg_replicate:nn { #2 }   { ,135 }

    prg_replicate:nn { #2 }   { ,225 }

    prg_replicate:nn { #2 }   { ,270 }

    prg_replicate:nn { #2 }   { ,315 }

   }

  tl_if_exist:NTF #1

   {

    msg_error:nnx {genlist}{exist}{token_to_str:N #1}

   }

   {

    tl_new:N #1

    tl_set_eq:NN #1 l_tmpa_tl

   }

 }



msg_new:nnnn {genlist}{exist}

 {

  Control~sequence~#1~already~defined

 }

 {

  The~control~sequence~#1~is~already~defined,~choose~a~different~name

 }



ExplSyntaxOff



generatelist{ONE}{1}

generatelist{TWO}{2}

generatelist{THREE}{3}

generatelist{FOUR}{4}



generatelist{box}{10} % this raises an error



begin{document}



ONE



TWO



THREE



FOUR



end{document}

A classical implementation, which shows why expl3 is preferable.

documentclass{article}



makeatletter

newcommand{genlist@aux}[2]{%

  ifnum#1>0

    ,#2%

    expandafter@firstofone

  else

    expandafter@gobble

  fi

  {expandaftergenlist@auxexpandafter{thenumexpr#1-1}{#2}}%

}



newcommand{generatelist}[2]{%

  @ifdefinable#1{genlist@main{#1}{#2}}%

}

newcommand{genlist@main}[2]{%

  edef#1{%

    45%

    expandaftergenlist@auxexpandafter{thenumexpr#2-1}{45}%

    expandaftergenlist@auxexpandafter{thenumexpr#2-1}{90}%

    genlist@aux{#2}{135}%

    genlist@aux{#2}{225}%

    genlist@aux{#2}{270}%

    genlist@aux{#2}{315}%

  }%

}

makeatother



generatelist{ONE}{1}

generatelist{TWO}{2}

generatelist{THREE}{3}

generatelist{FOUR}{4}



%generatelist{box}{10} % this would raise an error



begin{document}



ONE



TWO



THREE



FOUR



end{document}