Padovan n-step number sequences: Difference between revisions

=={{header|Mathematica}}/{{header|Wolfram Language}}==

<lang Mathematica>ClearAll[Padovan]

Padovan[2,tmax_]:=Module[{start,a,m},

start={1,1,1};

start=MapIndexed[a[#2[[1]]]==#1&,start];

RecurrenceTable[{a[m]==a[m-2]+a[m-3]}~Join~start,a, {m,tmax}]

]

Padovan[n_,tmax_]:=Module[{start,eq,a,m},

start=Padovan[n-1,n+1];

start=MapIndexed[a[#2[[1]]]==#1&,start];

eq=Range[2,n+1];

eq=Append[start,a[m]==Total[a[m-#]&/@eq]];

RecurrenceTable[eq,a, {m,tmax}]

]

Padovan[2,15]

Padovan[3,15]

Padovan[4,15]

Padovan[5,15]

Padovan[6,15]

Padovan[7,15]

Padovan[8,15]</lang>

{{out}}

<pre>{1,1,1,2,2,3,4,5,7,9,12,16,21,28,37}

{1,1,1,2,3,4,6,9,13,19,28,41,60,88,129}

{1,1,1,2,3,5,7,11,17,26,40,61,94,144,221}

{1,1,1,2,3,5,8,12,19,30,47,74,116,182,286}

{1,1,1,2,3,5,8,13,20,32,51,81,129,205,326}

{1,1,1,2,3,5,8,13,21,33,53,85,136,218,349}

{1,1,1,2,3,5,8,13,21,34,54,87,140,225,362}</pre>