A054254 a(n) is n plus the minimum of the a(i)*a(n-i) of the previous i = 1..n-1.

0, 1, 2, 5, 8, 13, 19, 26, 34, 43, 53, 64, 76, 89, 103, 118, 134, 151, 169, 188, 208, 229, 251, 274, 298, 323, 349, 376, 404, 433, 463, 494, 526, 559, 593, 628, 664, 701, 739, 778, 818, 859, 901, 944, 988, 1033, 1079, 1126, 1174, 1223, 1273

Offset: 0

Author

N. J. A. Sloane, May 04 2000

Keywords

• nonn
• easy

Comments

If in the Maple code "if n<=2 then n" were replaced by "if n<=1 then n", then the sequence would become the triangular numbers A000217. In general, if the Maple code were "if n<=k then n" for some given k > 0 then a(n) would be n if n <= k, n + k*(n-k) if k <= n <= 2k and n*(n+1)/2 - k*(k-1) if 2k <= n. - Henry Bottomley, Mar 30 2001

Examples

			a(3) = 3 + 1*2 = 5,
a(4) = 4 + 2*2 = 8 since 2*2 < 1*5,
a(5) = 5 + 1*8 = 13 since 1*8 < 2*5.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

Maple

A054254 := proc(n) local i,j; option remember; if n<=2 then n else j := 10^100; 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; fi; end proc;

Mathematica

Join[{0, 1, 2, 5}, LinearRecurrence[{3, -3, 1}, {8, 13, 19}, 50]] (* Jean-François Alcover, Apr 29 2023 *)

Formula

For n > 3: a(n) = (n^2 + n - 4)/2 = A034856(n-1) = A000217(n) - 2 = A000297(n-3) - A000297(n-2).

For n > 4: a(n) = a(n-1) + n.

G.f.: x*(x^2-x+1)*(x^3-x^2-1)/(x-1)^3. - R. J. Mathar, Dec 09 2009

Extensions

More specific name from R. J. Mathar, Dec 09 2009