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A054254 a(n) is n plus the minimum of the a(i)*a(n-i) of the previous i=1..n-1. 2


%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" was replaced by "if n<=1 then n", then the sequence would become the triangular numbers A000217. In general, if the Maple code was "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

%F 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.

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

%K nonn

%O 0,3

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

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

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Last modified September 18 16:05 EDT 2020. Contains 337169 sequences. (Running on oeis4.)