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 A262123 a(1) + a(2) + ... + a(n) is the representation as a sum of n squares of the smallest integer needing n squares (using the greedy algorithm). 0
 1, 1, 1, 4, 16, 144, 7056, 13046544, 42600214749456, 453694852221644777216198544 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS E. Lemoine, Décomposition d'un nombre entier N en ses puissances nièmes maxima, C. R. Acad. Sci. Paris, Vol. 95, pp. 719-722, 1882. FORMULA a(1)=1; for n>1, if s = a(1)+a(2)+...+a(n-1) then a(n+1) = floor((s+1)/2)^2. a(1)+...+a(n) = A006892(n). a(1)=a(2)=a(3)=1, a(4)=4; for n>=4, a(n+1) = ( a(n)/2+sqrt(a(n)) )^2. EXAMPLE 23 =16+4+1+1+1 is the first number to need 5 squares for its greedy decomposition, so a(1)=1,a(2)=1,a(3)=1,a(4)=4,a(5)=16. MAPLE a:=n->if n=1 then 1 else s:=add(a(k), k=1..n-1); floor((s+1)/2)^2 fi; MATHEMATICA a[1] = 1; a[n_] := a[n] = Floor[(Total[Array[a, n-1]]+1)/2]^2; Array[a, 11] (* Jean-François Alcover, Oct 05 2015 *) PROG (Python) def list_a(n): ....list=[1, 1, 1, 4]; root=2; length=4 ....while length

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Last modified May 7 19:23 EDT 2021. Contains 343652 sequences. (Running on oeis4.)