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SUMMARY:Russell Jay Hendel (Towson University)
DTSTART:20220526T200000Z
DTEND:20220526T202500Z
DTSTAMP:20260423T011341Z
UID:CANT2022/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/43/
 ">A system of 4 simultaneous recursions: Generalization of  Ledin-Shannon-
 Ollerton</a>\nby Russell Jay Hendel (Towson University) as part of Combina
 torial and additive number theory (CANT 2022)\n\n\nAbstract\nThis paper fu
 rther generalizes a recent result of Shannon and Ollerton who resurrected 
 an old identity due to Ledin.  \nThis paper generalizes the Ledin-Shannon-
 Ollerton result to all metallic sequences. The results give closed formula
 s for the sum of products of powers of the first $n$ integers with the fir
 st $n$ members of the metallic sequence. \nThree key innovations of this p
 aper are (i) reducing the proof of the generalization to the solution of  
 a system of 4 simultaneous recursions\;\n(ii) skillful use of the shift op
 eration to prove equality of polynomials\; and (iii) new OEIS sequences\na
 rising from the coefficients of  the four polynomial\nfamilies satisfying 
 the four simultaneous recursions.\n
LOCATION:https://researchseminars.org/talk/CANT2022/43/
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