Three short elementary proofs establish the conjectured homogeneous recurrence for OEIS A002627 from its defining inhomogeneous recurrence.
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The conjectured recurrence for A176677 is established by showing its generating function satisfies a first-order linear ODE whose coefficients yield the recurrence upon series expansion.
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Three short proofs of Mathar's 2014 conjecture for OEIS A002627
Three short elementary proofs establish the conjectured homogeneous recurrence for OEIS A002627 from its defining inhomogeneous recurrence.
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A short proof of Mathar's 2016 recurrence conjecture for OEIS A176677
The conjectured recurrence for A176677 is established by showing its generating function satisfies a first-order linear ODE whose coefficients yield the recurrence upon series expansion.