A054254 - OEIS

%I #19 Apr 29 2023 17:42:45

%S 0,1,2,5,8,13,19,26,34,43,53,64,76,89,103,118,134,151,169,188,208,229,

%T 251,274,298,323,349,376,404,433,463,494,526,559,593,628,664,701,739,

%U 778,818,859,901,944,988,1033,1079,1126,1174,1223,1273

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

%C 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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

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

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

%F G.f.: x*(x^2-x+1)*(x^3-x^2-1)/(x-1)^3. - _R. J. Mathar_, Dec 09 2009

%e a(3) = 3 + 1*2 = 5,

%e a(4) = 4 + 2*2 = 8 since 2*2 < 1*5,

%e a(5) = 5 + 1*8 = 13 since 1*8 < 2*5.

%p 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;

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

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, May 04 2000

%E More specific name from _R. J. Mathar_, Dec 09 2009