mkl:= proc(i,l) local ll, mn, x; ll:= applyop(x->x+1, irem (i,5)+1, l); mn:= min(ll[]); `if`(mn=0, ll, map(x->x-mn, ll)) end:
g:= proc (n,i,t) if n<0 then 0 elif n=0 then `if`(t[2]=t[5] and t[3]=t[4] and t[5]t[4], 0, g(n-2*(t[4]-t[3]), 1, [t[1], t[2], t[4], t[4], t[5]])) else g(n,i,t):= g(n, i-1, t) + g(n-i, i, mkl(i,t)) fi end:
a:= n-> g(5*n, 5*n, [0,0,0,0,0]):
seq(a(n), n=1..15); # Alois P. Heinz, Jul 02 2009
mkl[i_, l_List] := Module[{ll, mn, x}, ll = MapAt[#+1&, l, Mod[i, 5]+1]; mn = Min[ll]; If[mn == 0, ll, ll-mn]]; g[n_, i_, t_List] := g[n, i, t] = Which[n<0, 0, n == 0, If[t[[2]] == t[[5]] && t[[3]] == t[[4]] && t[[5]] < t[[1]] && t[[1]] <= t[[3]], 1, 0], True, Which[i == 0, 0, i == 1, g[0, 0, {t[[1]], t[[2]]+n, t[[3]], t[[4]], t[[5]]}], i == 2, If[t[[3]] > t[[4]], 0, g[n-2*(t[[4]] - t[[3]]), 1, t[[{1, 2, 4, 4, 5}]]]], True, g[n, i, t] = g [n, i-1, t] + g[n-i, i, mkl[i, t]]]]; a[n_] := a[n] = g[5*n, 5*n, {0, 0, 0, 0, 0}]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 32}] (* Jean-François Alcover, Dec 23 2015, after Alois P. Heinz *)
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