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 A025427 Number of partitions of n into 3 nonzero squares. 37
 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 2, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 2, 0, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 0, 1, 3, 0, 1, 2, 0, 2, 0, 1, 2, 0, 0, 1, 3, 1, 1, 2, 1, 0, 1, 1, 2, 2, 1, 2, 1, 0, 0, 3, 1, 2, 1, 0, 3, 0, 1, 3, 2, 1, 0, 1, 2, 0, 1, 1, 2, 3, 0, 3, 2, 0, 1, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,28 COMMENTS The non-vanishing values a(n) give the multiplicities for the numbers n appearing in A000408. See also A024795 where these numbers n are listed a(n) times. For the primitive case see A223730 and A223731. - Wolfdieter Lang, Apr 03 2013 LINKS R. J. Mathar and R. Zumkeller, Table of n, a(n) for n = 0..10000, first 5592 terms from R. J. Mathar FORMULA a(A004214(n) = 0; a(A000408(n) > 0; a(A025414(n)) = n and a(m) != n for m < A025414(n). - Reinhard Zumkeller, Feb 26 2015 a(4n) = a(n). This is because if a number divisible by 4 is the sum of three squares, each of those squares must be even. - Robert Israel, Mar 09 2016 a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} A010052(i) * A010052(k) * A010052(n-i-k). - Wesley Ivan Hurt, Apr 19 2019 a(n) = [x^n y^3] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019 EXAMPLE a(27) = 2 because  1^2 + 1^2 + 5^2 = 27  = 3^2 + 3^2 + 3^2. The second representation is not primitive (gcd(3,3,3) = 3 not 1). MAPLE A025427 := proc(n)     local a, x, y, zsq ;     a := 0 ;     for x from 1 do         if 3*x^2 > n then             return a;         end if;         for y from x do             if x+2*y^2 > n then                 break;             end if;             zsq := n-x^2-y^2 ;             if issqr(zsq) then                 a := a+1 ;             end if;         end do:     end do: end proc: # R. J. Mathar, Sep 15 2015 MATHEMATICA Count[PowersRepresentations[#, 3, 2], pr_ /; (Times @@ pr) > 0]& /@ Range[0, 120] (* Jean-François Alcover, Jan 30 2018 *) PROG (Haskell) a025427 n = sum \$ map f zs where    f x = sum \$ map (a010052 . (n - x -)) \$                    takeWhile (<= div (n - x) 2) \$ dropWhile (< x) zs    zs = takeWhile (< n) \$ tail a000290_list -- Reinhard Zumkeller, Feb 26 2015 CROSSREFS Cf. A000408, A024795, A223730 (multiplicities for the primitive case). - Wolfdieter Lang, Apr 03 2013 Column k=3 of A243148. Cf. A000290, A010052, A004214, A025321, A025414, A025426. Sequence in context: A089233 A066620 A219023 * A245963 A291375 A033778 Adjacent sequences:  A025424 A025425 A025426 * A025428 A025429 A025430 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified June 25 11:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)