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%I #14 Apr 03 2020 16:44:44
%S 1,2,5,9,15,31,52,89,164,289,479,973,1625,2773,5099,8975,15045,30181,
%T 50615,86617,159593,281219,469648,946753,1581150,2698155,4961354,
%U 8732703,14638814,29366143,49248426,84278373,155284022,273626121,456980910,921190705,1538473662
%N a(n) = n + max{ a(i)*a(n-i) ; 1 <= i <= n-1 }, a(n) = n for n <= 2.
%H Alois P. Heinz, <a href="/A054253/b054253.txt">Table of n, a(n) for n = 1..2000</a>
%e a(5) = 5 plus the maximum of {1*2,2*5} = 5+10=15.
%e a(6) = 6 plus the maximum of {1*15,2*9,5*5} = 6+25=31.
%p A054253 := proc(n) local i,j; option remember; if n<=2 then n else j := 0; for i from 1 to n-1 do if procname(i)*procname(n-i) >= j then j := procname(i)*procname(n-i); end if; end do; n+j; end if; end proc;
%p # second Maple program:
%p a:= proc(n) option remember; n +`if`(n>2,
%p max(seq(a(i)*a(n-i), i=1..n/2)), 0)
%p end:
%p seq(a(n), n=1..42); # _Alois P. Heinz_, Apr 03 2020
%t a[n_] := a[n] = If[n <= 2, n, n + Max[a[#] a[n-#]& /@ Range[n-1]]];
%t Array[a, 33] (* _Jean-François Alcover_, Apr 03 2020 *)
%K nonn
%O 1,2
%A _N. J. A. Sloane_, May 04 2000
%E More specific name and examples from _M. F. Hasler_, Dec 08 2009 and _R. J. Mathar_, Dec 09 2009
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