(∑_(x=1)^89)((Sin[x °])^6) // Simplify

$RecursionLimit=∞;
Clear[f];
f[{_}]=0;
f[{n_,_}] := n;
f[{1,0,n_}] := n+1;
f[{1,a_,b_}] := 1+3a+b;
f[{n_,0,0}] := (2^(n+1))+n-2;
f[{0, s___}] := f[{s}];
f[s_List]:= f[s] = Max[
Max[Table[If[s[[i]]==0,0,
ns=s; ns[[i]]-=1; ns[[i+1]]+=2; f[ns]+1
], {i, Length[s]-1}]],
Max[Table[If[s[[i]]==0,0,
ns=s; ns[[i]]-=1; {ns[[i+1]], ns[[i+2]]}={ns[[i+2]], ns[[i+1]]}; f[ns]+1
], {i, Length[s]-2}]]
];
f[s___] := f[{s}]

f[1,1]

f[1,1,1]

f[1,1,1,1]

f[1,0,0,1,1]

f[1,2,30]

f[1,0,1,1,1]

?f