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 A156384 The number of solutions to x^2 + y^2 + 2*z^2 = n in nonnegative integers x,y,z. 3
 1, 2, 2, 2, 3, 2, 2, 2, 2, 4, 4, 2, 4, 4, 0, 2, 3, 4, 6, 4, 4, 2, 4, 2, 2, 6, 4, 6, 6, 2, 0, 4, 2, 6, 8, 2, 7, 6, 4, 2, 4, 4, 6, 6, 4, 6, 0, 4, 4, 6, 6, 4, 10, 4, 6, 6, 0, 6, 10, 4, 6, 6, 0, 6, 3, 4, 8, 8, 8, 4, 6, 2, 6, 10, 4, 6, 10, 4, 0, 4, 4, 8, 14, 6, 6, 8, 4, 6, 4, 6, 10, 6, 6, 6, 0, 2, 2, 12, 8, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also, the number of 4X4 matrices composed of squares of integers, symmetric under 90 degree rotation, with all rows summing to n. Such matrices have the form: z^2 x^2 y^2 z^2 y^2 z^2 z^2 x^2 x^2 z^2 z^2 y^2 z^2 y^2 x^2 z^2 with x^2 + y^2 + 2*z^2 = n. LINKS FORMULA a(n) = ( A014455(n) + 2*A033715(n) + A004018(n) + A000122(n/2) + 2*A000122(n) + A000007(n) )/8. - Max Alekseyev, Sep 29 2012 G.f.: (1 + theta_3(q))^2*(1 + theta_3(q^2))/8, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 01 2018 EXAMPLE All matrices for n=9: ...0.0.9.0...0.9.0.0...4.0.1.4...4.1.0.4 ...9.0.0.0...0.0.0.9...1.4.4.0...0.4.4.1 ...0.0.0.9...9.0.0.0...0.4.4.1...1.4.4.0 ...0.9.0.0...0.0.9.0...4.1.0.4...4.0.1.4 CROSSREFS Cf. A213024 Sequence in context: A175064 A104564 A160764 * A306249 A064656 A270776 Adjacent sequences:  A156381 A156382 A156383 * A156385 A156386 A156387 KEYWORD nonn AUTHOR R. H. Hardin Feb 09 2009 EXTENSIONS More general definition from Max Alekseyev, Sep 29 2012 STATUS approved

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Last modified November 24 04:08 EST 2020. Contains 338607 sequences. (Running on oeis4.)