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Let A(n,m) be the number of solutions of ∑k=−nnϵkk=m where each ϵk∈{0,1}. We determine the asymptotic behavior of A(n,m) for m=o(n3/2), extending results of van Lint and of Entringer

international journal of mathematics and mathematical sciences

On the representation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$m$"><mml:mi>m</mml:mi></mml:math>as<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\sum_{k=-n}^n \epsilon_k k$"><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mi>n</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mi>ϵ</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mi>k</mml:mi></mml:mrow></mml:math>

On the representation ofmas∑k=−nnϵkk