A054253 a(n) = n + max{ a(i)*a(n-i) ; 1 <= i <= n-1 }, a(n) = n for n <= 2.

1, 2, 5, 9, 15, 31, 52, 89, 164, 289, 479, 973, 1625, 2773, 5099, 8975, 15045, 30181, 50615, 86617, 159593, 281219, 469648, 946753, 1581150, 2698155, 4961354, 8732703, 14638814, 29366143, 49248426, 84278373, 155284022, 273626121, 456980910, 921190705, 1538473662

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..2000

Example

a(5) = 5 plus the maximum of {1*2,2*5} = 5+10=15.
a(6) = 6 plus the maximum of {1*15,2*9,5*5} = 6+25=31.

Maple

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;
# second Maple program:
a:= proc(n) option remember; n +`if`(n>2,
      max(seq(a(i)*a(n-i), i=1..n/2)), 0)
    end:
seq(a(n), n=1..42);  # Alois P. Heinz, Apr 03 2020

Mathematica

a[n_] := a[n] = If[n <= 2, n, n + Max[a[#] a[n-#]& /@ Range[n-1]]];
Array[a, 33] (* Jean-François Alcover, Apr 03 2020 *)

Crossrefs

Sequence in context: A339554 A274355 A351100 * A045649 A267694 A024519

Adjacent sequences: A054250 A054251 A054252 * A054254 A054255 A054256

Keyword

nonn

Author

N. J. A. Sloane, May 04 2000

Extensions

More specific name and examples from M. F. Hasler, Dec 08 2009 and R. J. Mathar, Dec 09 2009

Status

approved